Related papers: An inverse problem in quantum statistical physics
Recent research on the fundamentals of statistical mechanics has led to an interesting discovery [1-3]: With locally nonchaotic barriers, as Boltzmann's H-theorem is inapplicable, there exist nontrivial non-thermodynamic systems that can…
In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs)…
For a system randomly prepared in a number of quantum states, we present a lower bound for the distinguishability of the quantum states, that is, the success probability of determining the states in the form of entropy. When the states are…
We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and…
There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to exp(-E/kT) where E is…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I…
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
Time reversal symmetry is a fundamental property of many quantum mechanical systems. The relation between statistical physics and time reversal is subtle and not all statistical theories conserve this particular symmetry, most notably…
The expression for the density operator of the damped harmonic oscillator is derived from the master equation in the framework of the Lindblad theory for open quantum systems. Then the von Neumann entropy and effective temperature of the…
This letter examines the consequences of a recently proposed modification of the postulate of equal {\it a priori} probability in quantum statistical mechanics. This modification, called the {\it quantum microcanonical postulate} (QMP),…
It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of…
Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences such as the strong…
Dynamical inverse problem of representation theory, which has its origin in a classical paper of E.P.Wigner on a determination of commutation relations of quantum mechanical quantities by the quantum dynamical equations, is illustrated on…
In quantum field theory, there exist states in which the expectation value of the energy density for a quantized field is negative. These negative energy densities lead to many problems. Although quantum field theory introduces negative…