Related papers: An inverse problem in quantum statistical physics
The dynamics of an atom on the Jaynes-Cummings model has been studied by an atomic inversion, von Neumann entropy and so on. In this letter, we will treat the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics and…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…
We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists…
In an innovative inverse-problem construction the measured, experimental energies $E_1$, $E_2$, ...$E_N$ of a quantum bound-state system are assumed fitted by an N-plet of zeros of a classical orthogonal polynomial $f_N(E)$. We reconstruct…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
A microscopic understanding of the thermodynamic entropy in quantum systems has been a mystery ever since the invention of quantum mechanics. In classical physics, this entropy is believed to be the logarithm of the volume of phase space…
We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covariance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions.…
By using the quantum maximum entropy principle we formally derive, from a underlying kinetic description, isothermal (hydrodynamic and diffusive) quantum fluid equations for particles with Fermi-Dirac and Bose-Einstein statistics. A…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Recently, many fundamental and important results in statistical decision theory have been extended to the quantum system. Quantum Hunt-Stein theorem and quantum locally asymptotic normality are typical successful examples. In the present…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…