NUCLEI AND MESOSCOPIC PHYSICS: Workshop on Nuclei and Mesoscopic Physics: WNMP 2004

Universality in few‐body systems with large scattering length
View Description Hide DescriptionEffective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model‐independent calculations. Particularly interesting are few‐body systems with short‐range interactions and large two‐body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three‐body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four‐body system and N‐boson droplets in two spatial dimensions will also be addressed.

Correlated Gaussian method for dilute bosonic systems
View Description Hide DescriptionThe weakly interacting trapped Bose gases have been customarily described using the mean‐field approximation in the form of the Gross‐Pitaevskii equation. The mean‐field approximation, however, has certain limitations, in particular it can not describe correlations between particles. We introduce here an alternative variational approach, based on the correlated Gaussian method, which in its simplest form is as fast and simple as the mean‐field approximation, but which allows successive improvements of the trial wave‐function by including correlations between particles.

Simulations of Dilute Fermi Gases
View Description Hide DescriptionDilute atomic Fermi gases are the subject of much current theoretical and experimental interest. Atomic gases have been cooled to temperatures much lower than the Fermi energy, and initial measurements of their properties have been achieved. We describe Quantum Monte Carlo calculations of the ground‐state properties of these intriguing systems, from the weak‐coupling regime described by BCS theory to the strong‐coupling regime where the atoms pair into weakly‐interacting dimers. We describe ground‐state properties and also calculations of the lowest spin‐excitations in these systems. Important directions for future work are also highlighted.

Bridging quantum chemistry and nuclear structure theory: Coupled‐cluster calculations for closed‐ and open‐shell nuclei
View Description Hide DescriptionWe review basic elements of the single‐reference coupled‐cluster theory and discuss large scale ab initio calculations of ground and excited states of ^{15}O, ^{16}O, and ^{17}O using coupled‐cluster methods and algorithms developed in quantum chemistry. By using realistic two‐body interactions and the renormalized form of the Hamiltonian obtained with a no‐core G‐matrix approach, we obtain the converged results for ^{16}O and promising preliminary results for ^{15}O and ^{17}O at the level of two‐body interactions. The calculated properties other than energies include matter density, charge radius, and charge form factor. The relatively low costs of coupled‐cluster calculations, which are characterized by the low‐order polynomial scaling with the system size, enable us to probe large model spaces with up to 7 or 8 major oscillator shells, for which non‐truncated shell‐model calculations for nuclei with A = 15 17 active particles are presently not possible. We argue that the use of coupled‐cluster methods and computer algorithms developed by quantum chemists to calculate properties of nuclei is an important step toward the development of accurate and affordable many‐body theories that cross the boundaries of various physical sciences.

Multi‐level and two‐level models of the decay out of superdeformed bands
View Description Hide DescriptionWe compare a multi‐level statistical model with a two‐level model for the decay out of superdeformed rotational bands in atomic nuclei. We conclude that while the models depend on different dimensionless combinations of the input parameters and differ in certain limits, they essentially agree in the cases where experimental data is currently available. The implications of this conclusion are discussed.

Normal persistent currents and gross shell structure at high spin
View Description Hide DescriptionThe magnetic response of metal clusters and the rotational response of nuclei are determined by strong normal persistent currents, the influence of which can be understood in terms of classical periodic orbits. The semiclassic Periodic Orbit Theory also explains the gross shell structure of the binding energies and the shapes of nuclei and clusters. The relevant properties, which are measured for nuclei, are explained.

Multi‐vortex phase transitions in rotating Bose‐Einstein condensates
View Description Hide DescriptionWe study the lowest energy states of a weakly interacting trapped atomic Bose‐Einstein condensate in both quantum and classical cases. An analytic expression for the ground‐state wavefunction of a rotating Gross‐Pitaevskii condensate of trapped atoms describes the onset of vorticity in an accelerated trap, starting from the vortex entry followed by formation of growing symmetric Wigner molecules. Within a unified picture, it explains the staircase of the angular momentum jumps and the behavior of the bosonic occupancies observed in numerical and variational studies. The similarity of this behavior and mesoscopic superconductors is discussed.

SU(4) Model of High‐Temperature Superconductivity: Manifestation of Dynamical Symmetry in Cuprates
View Description Hide DescriptionThe mechanism that leads to high‐temperature superconductivity in cuprates remains an open question despite intense study for nearly two decades. Here, we introduce an SU(4) model for cuprate systems having many similarities to dynamical symmetries known to play an important role in nuclear structure physics and in elementary particle physics. Analytical solutions in three dynamical symmetry limits of this model are found: an SO(4) limit associated with antiferromagnetic order; an SU(2) limit that may be interpreted as a d‐wave pairing condensate; and an SO(5) limit that may be interpreted as a doorway state between the antiferromagnetic order and the superconducting order. It is demonstrated that with a slightly broken SO(5) but under constraint of the parent SU(4) symmetry, the model is capable of describing the rich physics that is crucial in explaining why cuprate systems that are antiferromagnetic Mott insulators at half filling become superconductors through hole doping.

The Kondo Effect and Controlled Spin Entanglement in Coupled Double‐Quantum‐Dots
View Description Hide DescriptionSemiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.

Shape Transition and Shape Coexistence in Atomic Clusters and Nuclei
View Description Hide DescriptionWe investigate the signature of shape transition and shape coexistence in small atomic clusters and other mesoscopic systems, such as atomic nuclei. One of the best known examples is the prolate‐compact shape transition/coexistence phenomenon observed in mobility experiments on Si clusters.[1] Using a hierarchical strategy that features an extensive tight‐binding‐based search of the energy surface, followed by a full density functional theory investigation of the most stable structures, we recently determined the lowest‐energy clusters across the range n=2 to 28.[2] The calculated properties of these clusters are in very good agreement with available measurements of dissociation energies, ionization energies and ion mobilities, providing strong evidence that these structures are the ones found in experiments. The calculations clearly exhibit a transition in the relative stability of prolate and compact clusters between n=25 and 26, coinciding exactly with the experimental behavior. The lowest energy prolate and compact structures are found almost degenerate, justifying the coexistence of shapes observed in the experiment. The binding energy per atom of the ground states vs N ^{−1/3} exhibits a long plateau in the transition/coexistence region, suggesting that this phenomenon may be related to a relatively small surface tension. Similar behavior was recently found in the isotope 152 of the nucleus of the element Sm, for which the ground sate, J ^{π} = 0^{+}, is known to be very deformed, and the first excited J ^{π} = 0^{+}, is compact. A similar signature in the binding energy per atom of the Sm isotopes can be also extracted from the available experimental data.

Computational Nanotechnology: From Clusters to Devices
View Description Hide DescriptionThis contribution describes recent applications of supercomputers to describing phenomena occurring on the nanometer scale, which evade direct experimental observation. Dependable ab initio calculations can determine, whether all‐carbon nanostructures may become metallic or even magnetic. Computer simulations help us understand, how to design nanostructures with unusual properties, such as high thermal conductivity, thermal contraction, and even nanoscale bonding systems for NEMS devices.

Regular versus chaotic dynamics in closed systems of interacting Fermi particles
View Description Hide DescriptionWe discuss dynamical properties of strongly interacting Fermi‐particles. Main attention is paid to the evolution of wave packets in the many‐particle basis of non‐interacting particles. Specifically, we analyze the time dependence of the return probability and the Shannon entropy of packets. We start with the model of two‐body random interaction which allows us to obtain analytical expression for the time dependence of the above quantities. Analytical results are compared with numerical data obtained in direct simulation of the wave packet dynamics. To understand to what extent these results are generic, we have considered the spin model of a quantum computation with a non‐random (dynamical) interaction between spins. We have found that the linear increase of the Shannon entropy observed in the two‐body random model, occurs, under some conditions, in the dynamical model. Finally, we have analyzed the role of weak external perturbation taken in the form of static disorder.

Quantum Chaos generates Regularities
View Description Hide DescriptionThe mechanism of the dominance (preponderance) of the 0^{+} ground state for random interactions is proposed to be the chaotic realization of the highest rotational symmetry. This is a consequence of a general principle on the chaos and symmetry that the highest symmetry is given to the ground state if sufficient mixing occurs in a chaotic way by a random interaction. Under this symmetry‐realization mechanism, the ground‐state parity and isospin can be predicted so that the positive parity is favored over the negative parity and the isospin T = 0 state is favored over higher isospin. It is further suggested how one can enhance the realization of highest symmetries within random interactions. Thus, chaos and symmetry are shown to be linked deeply.

Geometric aspects of the shell model
View Description Hide DescriptionWe study the spin‐dependent widths of random Hamiltonians and derive closed expressions for their distributions and the correlations between them. This is facilitated by the introduction of linear combinations of two‐body operators that are orthogonal under the canonical scalar product for matrices. Considering six fermions in a single j‐shell, we find that the width of spin‐0 Hamiltonians exhibits a relatively large average value, relatively small fluctuations, and is strongly correlated to other low‐spin widths. The width of maximum spin in contrast has the largest average value and largest fluctuations. An approximate proportionality between spectral width and ground state energies explains the spin‐0 dominance in the shell model with random interactions.

Many‐particle localization by constructed disorder and quantum computing
View Description Hide DescriptionWe demonstrate the onset of strong localization in a one dimensional fermion system, where all particles are almost completely confined to their sites. The on‐site localization is obtained by constructing a bounded one‐parameter sequence of site energies that eliminates resonant hopping between both nearest and remote sites. In an infinite system the time during which all many‐particle states remain on‐site localized scales as a high power of the ratio of the bandwidth of site energies to the hopping integral. The results apply to a system of perpetually coupled qubits and demonstrate that such system can be used for quantum computing.

A Certain Localization Effect in Coupled Systems and Messages from the Crystal Sphere
View Description Hide DescriptionTwo theoretical studies are presented, both prompted by recent experiments. First, we investigate the time evolution of excitations in two chaotically coupled systems. There is a certain localization effect, because equipartition of the probability density or the energy is typically not reached. We use a random matrix model to give a generic explanation for this effect. Second, we derive a leading order Weyl formula for the elastic vibration spectrum of anisotropic quartz. This is non‐trivial due to the presence of different modes. We discuss a duality between one spherical billiard with anisotropy in configuration space and three non‐spherical billiards without anisotropy in slowness space.

Recent development in Deformed Gaussian Ensembles
View Description Hide DescriptionDeformed Gaussian Ensembles of Random Matrices are used to describe situations intermediate between fully chaotic complex quantum systems and regular ones. Such decriptions encompass the study of discrete symmetry breaking in nuclei, atoms and mesoscopic systems. In this short review we present several of the recent developments in this area. The deformation of Gaussian Ensembles is enforced through the use of the maximum entrpy principle with appropriate constraints. The resulting Deformed Gaussian Ensemble (DGE) is applied to study isospin symmetry breaking in nuclei, the metal‐insulator transition in condensed matter and in the evolution of level curvature distribution. More recently, this theory is applied to study the dependence of tunneling on the degree of chaoticity in the decay out of superdeformed bands in heavy nuclei. We derive and discuss the average level density of the DGE.

Level density of a Fermion gas: average growth, fluctuations, universality
View Description Hide DescriptionIt has been shown by H. Bethe more than 70 years ago that the number of excited states of a Fermi gas grows, at high excitation energies Q, like the exponential of the square root of Q. This result takes into account only the average density of single particle (SP) levels near the Fermi energy. It ignores two important effects, namely the discreteness of the SP spectrum, and its fluctuations. We show that the discreteness of the SP spectrum gives rise to smooth finite‐Q corrections. Mathematically, these corrections are associated to the problem of partitions of an integer. On top of the smooth growth of the many‐body density of states there are, generically, oscillations. An explicit expression of these oscillations is given. Their properties strongly depend on the regular or chaotic nature of the SP motion. In particular, we analyze their typical size, temperature dependence and probability distribution, with emphasis on their universal aspects.

Thermodynamic Analogy for Structural Phase Transitions
View Description Hide DescriptionWe investigate the relationship between ground‐state (zero‐temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature‐driven) phase transitions in standard thermodynamics. An analogy is found between (i) phase‐transitional distributions of the ground‐state related branch points of quantum Hamiltonians in the complex parameter plane and (ii) distributions of zeros of classical partition functions in complex temperatures. Our approach properly describes the first‐ and second‐order quantum phase transitions in the interacting boson model and can be generalized to finite temperatures.