Journal of Mathematical Physics: Most Recent Articles
http://scitation.aip.org/content/aip/journal/jmp?TRACK=RSS
Please follow the links to view the content.Inverse scattering transform of a new optical short pulse system
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904492?TRACK=RSS
<div><p>We focus our attention on the coupled short-pulse equation recently derived by Feng [J. Phys. A: Math. Theor. <span class="jp-bold">45</span>, 085202 (2012)] from a two-dimensional Bäcklund transformation of the Toda lattice equation. Investigating the prolongation structure of such a system, we unveil the hidden structural symmetry that governs the dynamics of the wave solutions to the system alongside with the corresponding Lax-pairs. As a matter of illustration, following the Wadati-Konno-Ichikawa scheme, we construct some solitary wave solutions to the system and study their interactions.</p></div>Wed, 24 Dec 2014 13:09:05 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904492?TRACK=RSSHermann T. Tchokouansi, Victor K. Kuetche and Timoleon C. Kofane2014-12-24T13:09:05ZA note on the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904836?TRACK=RSS
<div><p>We present a regularity criterion for the solutions to the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Navier-Stokes equations</span> based on the gradient of one velocity component. Starting with the method developed by Cao and Titi [“Global regularity criterion for the 3D <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Navier-Stokes equations</span> involving one entry of the velocity gradient tensor,” Arch. Ration. Mech. Anal. <span class="jp-bold">202</span>, 919–932 (2011)] for the case of one entry of the velocity gradient and using further some <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">inequalities</span> concerning the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">anisotropic</span> Sobolev spaces, we show as a main result that a weak solution <span class="jp-italic">u</span> is regular on (0, <span class="jp-italic">T</span>), <span class="jp-italic">T</span> > 0, provided that ∇<span class="jp-italic">u</span>
<span class="jp-sub">3</span> ∈ <span class="jp-italic">L<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">t</sup>
</span>(0, <span class="jp-italic">T</span>; <span class="jp-italic">L<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">s</sup>
</span>), where 2/<span class="jp-italic">t</span> + 3/<span class="jp-italic">s</span> = 3/2 + 3/(4<span class="jp-italic">s</span>) and <span class="jp-italic">s</span> ∈ (3/2, 2). It improves the known results for <span class="jp-italic">s</span> ∈ (3/2, 15/8).</p></div>Wed, 24 Dec 2014 13:09:01 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904836?TRACK=RSSZdeněk Skalák2014-12-24T13:09:01ZQuantization of borderline Levi conjugacy classes of orthogonal groups
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902381?TRACK=RSS
<div><p>We construct an equivariant quantization of a special family of Levi conjugacy classes of the complex orthogonal group <span class="jp-italic">SO</span>(<span class="jp-italic">N</span>), whose stabilizer contains a Cartesian factor <span class="jp-italic">SO</span>(2) × <span class="jp-italic">SO</span>(<span class="jp-italic">P</span>), 1 ⩽ <span class="jp-italic">P</span> < <span class="jp-italic">N</span>, <span class="jp-italic">P</span> ≡ <span class="jp-italic">N</span> mod 2.</p></div>Wed, 24 Dec 2014 13:08:53 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902381?TRACK=RSSThomas Ashton and Andrey Mudrov2014-12-24T13:08:53ZPosition-momentum uncertainty relations in the presence of quantum memory
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903989?TRACK=RSS
<div><p>A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.</p></div>Tue, 23 Dec 2014 15:54:37 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903989?TRACK=RSSFabian Furrer, Mario Berta, Marco Tomamichel, Volkher B. Scholz and Matthias Christandl2014-12-23T15:54:37ZTime-reversal symmetric resolution of unity without background integrals in open quantum systems
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904200?TRACK=RSS
<div><p>We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green’s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schrödinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over <span class="jp-italic">un</span>perturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.</p></div>Tue, 23 Dec 2014 15:39:00 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904200?TRACK=RSSNaomichi Hatano and Gonzalo Ordonez2014-12-23T15:39:00ZOn integration of a multidimensional version of n-wave type equation
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904485?TRACK=RSS
<div><p>We represent a version of multidimensional quasilinear partial differential equation (PDE) together with large manifold of particular solutions given in an integral form. The dimensionality of constructed PDE can be arbitrary. We call it the <span class="jp-italic">n</span>-wave type PDE, although the structure of its nonlinearity differs from that of the classical completely integrable (2+1)-dimensional <span class="jp-italic">n</span>-wave equation. The richness of solution space to such a PDE is characterized by a set of arbitrary functions of several variables. However, this richness is not enough to provide the complete integrability, which is shown explicitly. We describe a class of multi-solitary wave solutions in details. Among examples of explicit particular solutions, we represent a lump-lattice solution depending on five independent variables. In Appendix, as an important supplemental material, we show that our nonlinear PDE is reducible from the more general multidimensional PDE which can be derived using the dressing method based on the linear integral equation with the kernel of a special type (a modification of the <span class="capture-id">
<script xmlns="http://pub2web.metastore.ingenta.com/ns/" type="math/mml">
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mover>
<mml:mrow>
<mml:mi>∂</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>̄</mml:mo>
</mml:mrow>
</mml:mover>
</mml:math>
</script>
</span>-problem). The dressing algorithm gives us a key for construction of higher order PDEs, although they are not discussed in this paper.</p></div>Tue, 23 Dec 2014 13:46:40 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904485?TRACK=RSSA. I. Zenchuk2014-12-23T13:46:40ZStates that “look the same” with respect to every basis in a mutually unbiased set
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904317?TRACK=RSS
<div><p>A complete set of mutually unbiased bases (MUBs) in a <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Hilbert space</span> of dimension <span class="jp-italic">d</span> defines a set of <span class="jp-italic">d</span> + 1 orthogonal <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">measurements.</span> Relative to such a set, we define a <span class="jp-italic">MUB-balanced</span> state to be a pure state for which the list of probabilities of the <span class="jp-italic">d</span> outcomes of any of these <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">measurements</span> is independent of the choice of <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">measurement,</span> up to permutations. In this paper, we explicitly construct a MUB-balanced state for each prime power dimension <span class="jp-italic">d</span> for which <span class="jp-italic">d</span> = 3 (mod 4). These states have already been constructed by Appleby in unpublished notes, but our presentation here is different in that both the expression for the states themselves and the proof of MUB-balancedness are given in terms of the discrete Wigner function, rather than the density matrix or state vector. The discrete Wigner functions of these states are “rotationally symmetric” in a sense roughly analogous to the rotational symmetry of the energy eigenstates of a harmonic <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">oscillator</span> in the continuous two-dimensional phase space. Upon converting the Wigner function to a density matrix, we find that the states are expressible as real state vectors in the standard basis. We observe numerically that when <span class="jp-italic">d</span> is large (and not a power of 3), a histogram of the components of such a state vector appears to form a semicircular distribution.</p></div>Tue, 23 Dec 2014 13:46:18 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904317?TRACK=RSSIlya Amburg, Roshan Sharma, Daniel M. Sussman and William K. Wootters2014-12-23T13:46:18ZAmplitude modulation for the Swift-Hohenberg and Kuramoto-Sivashinski equations
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904486?TRACK=RSS
<div><p>Employing a harmonic balance technique inspired from the methods of <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Renormalization</span> Group and Multiple Scales [R. E. O’Malley, Jr. and E. Kirkinis. “A combined <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">renormalization</span> group-multiple scale method for singularly perturbed problems,” Stud. Appl. Math. <span class="jp-bold">124</span>(4), 383–410, (2010)], we derive the amplitude <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equations</span> for the Swift-Hohenberg and Kuramoto-Sivashinski <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equations</span> to arbitrary order in the context of roll patterns. This new and straightforward derivation improves previous attempts and can be carried-out with <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">symbolic computation</span> that minimizes effort and avoids error.</p></div>Tue, 23 Dec 2014 13:10:47 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904486?TRACK=RSSEleftherios Kirkinis and Robert E. O’Malley Jr.2014-12-23T13:10:47ZPeriodic discrete energy for long-range potentials
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903975?TRACK=RSS
<div><p>We consider periodic energy problems in Euclidean space with a special emphasis on long-range potentials that cannot be defined through the usual infinite sum. One of our main results builds on more recent developments of Ewald summation to define the periodic energy corresponding to a large class of long-range potentials. Two particularly interesting examples are the logarithmic potential and the Riesz potential when the Riesz parameter is smaller than the dimension of the space. For these examples, we use analytic continuation methods to provide concise formulas for the periodic kernel in terms of the Epstein Hurwitz Zeta function. We apply our energy definition to deduce several properties of the minimal energy including the asymptotic order of growth and the distribution of points in energy minimizing configurations as the number of points becomes large. We conclude with some detailed calculations in the case of one dimension, which shows the utility of this approach.</p></div>Tue, 23 Dec 2014 13:10:33 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903975?TRACK=RSSD. P. Hardin, E. B. Saff and B. Simanek2014-12-23T13:10:33ZExtensions of Hamiltonian systems dependent on a rational parameter
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904452?TRACK=RSS
<div><p>The technique of “extension” allows to build (<span class="jp-italic">d</span> + 2)-dimensional <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Hamiltonian systems</span> with a non-trivial <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">polynomial</span> in the momenta first integral of any given degree starting from a suitable <span class="jp-italic">d</span>-dimensional Hamiltonian. Until now, the application of the technique was restricted to integer values of a certain fundamental parameter determining the degree of the additional first integral. In this article, we show how the technique of extension can be generalized to any rational value of the same parameter. Several examples are given, among them the two uncoupled <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">oscillators</span> and a special case of the Tremblay-Turbiner-Winternitz system.</p></div>Tue, 23 Dec 2014 13:10:22 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904452?TRACK=RSSClaudia Maria Chanu, Luca Degiovanni and Giovanni Rastelli2014-12-23T13:10:22ZDecay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p-Laplacian
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904484?TRACK=RSS
<div><p>In this paper, we are concerned with the asymptotic behaviour of weak <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">solutions</span> to the initial <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary value problem</span> for a class of quasilinear hyperbolic equations with damping terms involving <span class="jp-italic">p</span>-Laplacian. By using the multiplier methods, we investigate the stability of weak <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">solutions</span> to the initial <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary value problem</span> and obtain explicit decay rate estimation depending on strain-caused stress term and damping terms.</p></div>Tue, 23 Dec 2014 13:09:45 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904484?TRACK=RSSYuhu Wu and Xiaoping Xue2014-12-23T13:09:45ZDirac equation with external potential and initial data on Cauchy surfaces
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902376?TRACK=RSS
<div><p>With this paper, we provide a mathematical review on the initial-value problem of the one-particle Dirac equation on space-like Cauchy hypersurfaces for compactly supported external potentials. We, first, discuss the physically relevant spaces of solutions and initial values in position and mass shell representation; second, review the action of the Poincaré group as well as gauge transformations on those spaces; third, introduce generalized Fourier transforms between those spaces and prove convenient Paley-Wiener- and Sobolev-type estimates. These generalized Fourier transforms immediately allow the construction of a unitary evolution operator for the free Dirac equation between the Hilbert spaces of square-integrable wave functions of two respective Cauchy surfaces. With a Picard-Lindelöf argument, this evolution map is generalized to the Dirac evolution including the external potential. For the latter, we introduce a convenient interaction picture on Cauchy surfaces. These tools immediately provide another proof of the well-known existence and uniqueness of classical solutions and their causal structure.</p></div>Mon, 22 Dec 2014 13:15:19 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902376?TRACK=RSSD.-A. Deckert and F. Merkl2014-12-22T13:15:19ZLoop Heisenberg-Virasoro Lie conformal algebra
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903990?TRACK=RSS
<div><p>Let <span class="jp-italic">HV</span> be the loop Heisenberg-Virasoro <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lie algebra</span> over ℂ with basis {<span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">α</span>,<span class="jp-italic">i</span>
</span>, <span class="jp-italic">H</span>
<span class="jp-sub">
<span class="jp-italic">β</span>,<span class="jp-italic">j</span>
</span>∣<span class="jp-italic">α</span>, <span class="jp-italic">β</span>, <span class="jp-italic">i</span>, <span class="jp-italic">j</span> ∈ ℤ} and brackets [<span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">α</span>,<span class="jp-italic">i</span>
</span>, <span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">β</span>,<span class="jp-italic">j</span>
</span>] = (<span class="jp-italic">α</span> − <span class="jp-italic">β</span>) <span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">α</span>+<span class="jp-italic">β</span>,<span class="jp-italic">i</span>+<span class="jp-italic">j</span>
</span>, [<span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">α</span>,<span class="jp-italic">i</span>
</span>, <span class="jp-italic">H</span>
<span class="jp-sub">
<span class="jp-italic">β</span>,<span class="jp-italic">j</span>
</span>] = − <span class="jp-italic">βH</span>
<span class="jp-sub">
<span class="jp-italic">α</span>+<span class="jp-italic">β</span>,<span class="jp-italic">i</span>+<span class="jp-italic">j</span>
</span>, [<span class="jp-italic">H</span>
<span class="jp-sub">
<span class="jp-italic">α</span>,<span class="jp-italic">i</span>
</span>, <span class="jp-italic">H</span>
<span class="jp-sub">
<span class="jp-italic">β</span>,<span class="jp-italic">j</span>
</span>] = 0. In this paper, a formal distribution <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lie algebra</span> of <span class="jp-italic">HV</span> is constructed. Then, the associated conformal algebra <span class="jp-italic">CHV</span> is studied, where <span class="jp-italic">CHV</span> has a ℂ[∂]-basis {<span class="jp-italic">L<span class="jp-sub">i</span>
</span>, <span class="jp-italic">H<span class="jp-sub">i</span>
</span>∣<span class="jp-italic">i</span> ∈ ℤ} with <span class="jp-italic">λ</span>-brackets [<span class="jp-italic">L<span class="jp-sub">i</span>
</span>
<span class="jp-sub">
<span class="jp-italic">λ</span>
</span>
<span class="jp-italic">L<span class="jp-sub">j</span>
</span>] = (∂ + 2<span class="jp-italic">λ</span>) <span class="jp-italic">L</span>
<span class="jp-sub">
<span class="jp-italic">i</span>+<span class="jp-italic">j</span>
</span>, [<span class="jp-italic">L<span class="jp-sub">i</span>
</span>
<span class="jp-sub">
<span class="jp-italic">λ</span>
</span>
<span class="jp-italic">H<span class="jp-sub">j</span>
</span>] = (∂ + <span class="jp-italic">λ</span>) <span class="jp-italic">H</span>
<span class="jp-sub">
<span class="jp-italic">i</span>+<span class="jp-italic">j</span>
</span>, [<span class="jp-italic">H<span class="jp-sub">i</span>
</span>
<span class="jp-sub">
<span class="jp-italic">λ</span>
</span>
<span class="jp-italic">L<span class="jp-sub">j</span>
</span>] = <span class="jp-italic">λL</span>
<span class="jp-sub">
<span class="jp-italic">i</span>+<span class="jp-italic">j</span>
</span>, and [<span class="jp-italic">H<span class="jp-sub">i</span>
</span>
<span class="jp-sub">
<span class="jp-italic">λ</span>
</span>
<span class="jp-italic">H<span class="jp-sub">j</span>
</span>] = 0. In particular, the conformal derivations of <span class="jp-italic">CHV</span> are determined. Finally, rank one conformal modules and ℤ-graded free intermediate series modules over <span class="jp-italic">CHV</span> are classified.</p></div>Mon, 22 Dec 2014 13:15:13 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903990?TRACK=RSSGuangzhe Fan, Yucai Su and Henan Wu2014-12-22T13:15:13ZNontrivial central extensions of 3-Lie algebras
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904018?TRACK=RSS
<div><p>We construct a series of infinite-dimensional 3-Lie algebras which include <span class="jp-italic">w</span>
<span class="jp-sub">∞</span> and <span class="jp-italic">SDiff</span>(<span class="jp-italic">T</span>
<sup xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sup>) 3-Lie algebras as subalgebras, and determine their nontrivial one-dimensional central extensions.</p></div>Mon, 22 Dec 2014 13:15:08 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904018?TRACK=RSSLu Ding, Zhaowen Yan, Huiping Zhang and Wei Zhang2014-12-22T13:15:08ZHistory dependent quantum random walks as quantum lattice gas automata
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903977?TRACK=RSS
<div><p>Quantum <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Random Walks</span> (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.</p></div>Mon, 22 Dec 2014 13:14:58 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903977?TRACK=RSSAsif Shakeel, David A. Meyer and Peter J. Love2014-12-22T13:14:58ZDipoles in graphene have infinitely many bound states
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904310?TRACK=RSS
<div><p>We show that in <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">graphene,</span> modelled by the two-dimensional <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Dirac</span> operator, charge distributions with non-vanishing <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">dipole moment</span> have infinitely many <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">bound states.</span> The corresponding <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">eigenvalues</span> accumulate at the edges of the gap faster than any power.</p></div>Fri, 19 Dec 2014 14:41:32 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904310?TRACK=RSSJean-Claude Cuenin and Heinz Siedentop2014-12-19T14:41:32ZSU(4) based classification of four-level systems and their semiclassical solution
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903000?TRACK=RSS
<div><p>We present a systematic method to classify the four-level system using <span class="jp-italic">
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">SU</span>
</span>(4) symmetry as the basis group. It is shown that this symmetry allows three dipole transitions which eventually leads to six possible configurations of the four-level system. Using a dressed atom approach, the semi-classical version of each configuration is exactly solved under rotating wave approximation and the symmetry among the Rabi oscillation among various <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">models</span> is studied.</p></div>Fri, 19 Dec 2014 14:35:32 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903000?TRACK=RSSSurajit Sen and Helal Ahmed2014-12-19T14:35:32ZBoundary conditions for the one-dimensional nonlinear nonstationary Boltzmann’s moment system equations
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902936?TRACK=RSS
<div><p>In this article, we put <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary conditions</span> for arbitrary approximation of the one-dimensional nonlinear nonstationary Boltzmann’s moment system <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equations.</span> We approximate microscopic <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Maxwell</span>
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary condition</span> for one-dimensional Boltzmann’s <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equation.</span> We formulate initial and <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary value problem</span> for six-moment Boltzmann’s system <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">equations</span> with <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Maxwell-Auzhan</span>
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">boundary conditions.</span>
</p></div>Thu, 18 Dec 2014 14:24:07 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902936?TRACK=RSSAuzhan Sakabekov and Yerkanat Auzhani2014-12-18T14:24:07ZQuantization of interface currents
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902377?TRACK=RSS
<div><p>At the interface of two two-dimensional quantum systems, there may exist interface currents similar to edge currents in quantum Hall systems. It is proved that these interface currents are macroscopically quantized by an integer that is given by the difference of the Chern numbers of the two systems. It is also argued that at the interface between two time-reversal invariant systems with half-integer spin, one of which is trivial and the other non-trivial, there are dissipationless spin-polarized interface currents.</p></div>Thu, 18 Dec 2014 14:15:00 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902377?TRACK=RSSMotoko Kotani, Hermann Schulz-Baldes and Carlos Villegas-Blas2014-12-18T14:15:00ZGlobal solutions of certain plasma fluid models in three-dimension
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903254?TRACK=RSS
<div><p>We consider several dispersive time-reversible plasma fluid models in 3 dimensions: the Euler-Poisson 2-fluid model, the relativistic Euler–Maxwell 1-fluid model, and the relativistic Euler–Maxwell 2-fluid model. In all of these models, we prove global stability of the constant background solutions, in the sense that small, smooth, and irrotational perturbations lead to smooth global solutions that decay as <span class="jp-italic">t</span> → ∞.</p></div>Wed, 17 Dec 2014 20:23:46 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903254?TRACK=RSSYan Guo, Alexandru D. Ionescu and Benoit Pausader2014-12-17T20:23:46ZEntanglement and the three-dimensionality of the Bloch ball
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903510?TRACK=RSS
<div><p>We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a <span class="jp-italic">d</span>-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.</p></div>Tue, 16 Dec 2014 20:25:01 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903510?TRACK=RSSLl. Masanes, M. P. Müller, D. Pérez-García and R. Augusiak2014-12-16T20:25:01ZThe action principle for dissipative systems
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903991?TRACK=RSS
<div><p>In the present work, we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lagrangian</span> for non-conservative systems, the <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lagrangian</span>
<span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">functions</span> proposed depend on mixed integer order and fractional order derivatives. As examples, we formulate a quadratic <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">Lagrangian</span> for a particle under a frictional force proportional to the velocity and to the classical problem of an <span xmlns="http://pub2web.metastore.ingenta.com/ns/" class="named-content">accelerated</span> point charge.</p></div>Tue, 16 Dec 2014 17:08:30 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903991?TRACK=RSSMatheus J. Lazo and Cesar E. Krumreich2014-12-16T17:08:30ZConformal killing tensors and covariant Hamiltonian dynamics
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902933?TRACK=RSS
<div><p>A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant <span class="jp-italic">G</span>(<span class="jp-italic">t</span>), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.</p></div>Tue, 16 Dec 2014 15:51:12 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902933?TRACK=RSSM. Cariglia, G. W. Gibbons, J.-W. van Holten, P. A. Horvathy and P.-M. Zhang2014-12-16T15:51:12ZDimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902380?TRACK=RSS
<div><p>We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann’s Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.</p></div>Tue, 16 Dec 2014 00:48:05 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4902380?TRACK=RSSMichael Dütsch, Klaus Fredenhagen, Kai Johannes Keller and Katarzyna Rejzner2014-12-16T00:48:05ZErratum: “Symmetry principles in quantum systems theory” [J. Math. Phys. 52, 113510 (2011)]
http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904017?TRACK=RSS
<div></div>Mon, 15 Dec 2014 15:05:06 GMThttp://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4904017?TRACK=RSSRobert Zeier and Thomas Schulte-Herbrüggen2014-12-15T15:05:06Z