Journal of Mathematical Physics, since 1960, publishes some of the best papers from outstanding mathematicians and physicists. It was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods suitable for such applications and for the formulation of physical theories.
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Subentropy is an entropylike quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the welldeveloped analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for minentropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classicalquantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally, we give an operational interpretation of subentropy within classical information theory.

“Low temperature” random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β → ∞. In this paper, we derive statistics for lowtemperature random matrices at the “soft edge,” which describes the extreme eigenvalues for many random matrix distributions. Specifically, new asymptotics are found for the expected value and standard deviation of the generalβ TracyWidom distribution. The new techniques utilize beta ensembles, stochastic differential operators, and Riccati diffusions. The asymptotics fit known hightemperature statistics curiously well and contribute to the larger program of generalβ random matrix theory.

We obtain the semiclassical expansion of the kernels and traces of Toeplitz operators with symbol on a symplectic manifold. We also give a semiclassical estimate of the distance of a Toeplitz operator to the space of selfadjoint and multiplication operators.

We consider β matrix models with real analytic potentials. Assuming that the corresponding equilibrium density ρ has a oneinterval support (without loss of generality σ = [−2, 2]), we study the transformation of the correlation functions after the change of variables λ i → ζ(λ i ) with ζ(λ) chosen from the equation ζ^{′}(λ)ρ(ζ(λ)) = ρ sc (λ), where ρ sc (λ) is the standard semicircle density. This gives us the “deformed” βmodel which has an additional “interaction” term. Standard transformation with the Gaussian integral allows us to show that the “deformed” βmodel may be reduced to the standard Gaussian βmodel with a small perturbation n ^{−1} h(λ). This reduces most of the problems of local and global regimes for βmodels to the corresponding problems for the Gaussian βmodel with a small perturbation. In the present paper, we prove the bulk universality of local eigenvalue statistics for both onecut and multicut cases.

Multitime wave functions are wave functions that have a time variable for every particle, such as . They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for noninteracting particles, it is a challenge to set up consistent multitime equations with interaction. We prove for a wide class of multitime Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multitime wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cutoff length δ > 0 is introduced (in the sense that the multitime wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multitime Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cutoff, the resulting multitime equations are interactionfree, which supports the conclusion expressed in the title.