Related papers: Gibbs states defined by biorthogonal sequences
In PT-quantum mechanics the generator of the dynamics of a physical system is not necessarily a self-adjoint Hamiltonian. It is now clear that this choice does not prevent to get a unitary time evolution and a real spectrum of the…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
Gibbs states of an infinite system of interacting quantum particles are considered. Each particle moves on a compact Riemannian manifold and is attached to a vertex of a graph (one particle per vertex). Two kinds of graphs are studied: (a)…
Gibbs states are known to play a crucial role in the statistical description of a system with a large number of degrees of freedom. They are expected to be vital also in a quantum gravitational system with many underlying fundamental…
I investigate the extent to which the description of quantum systems by Gibbs states can be justified purely on the basis of tomographic data, without recourse to theoretical concepts such as infinite ensembles, environments, information,…
We introduce a quantum generalization of classical kinetic Ising models, described by a certain class of quantum many body master equations. Similarly to kinetic Ising models with detailed balance that are equivalent to certain Hamiltonian…
The article deals with spin s=1 magnets. The symmetry conditions for normal and degenerate equilibrium states are defined and types of magnetic ordering found out. For each type of symmetry breaking the structure of source in the Gibbs…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…
We discuss certain generalization of the Hilbert space of states in noncommutaive quantum mechanics that, as we show, introduces magnetic monopoles into the theory. Such generalization arises very naturally in the considered model, but can…
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction…
The Hugenholz-Boltzmann-evolution is generalized to strongly interacting systems on the lattice. Under appropriate assumptions states stable under this evolution are shown to satify the KMS-condition. How far these assumptions are…
The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at…
We examine the theory of the KMS states on Pimsner algebras arising from multivariable unital C*-dynamical systems. As an application we show that Pimsner algebras of piecewise conjugate classical systems attain the same KMS states, even…
We study the KMS states on local quantum Cuntz-Krieger algebras associated to quantum graphs. Using their isomorphism to the Cuntz-Pimsner algebra of the quantum edge correspondence, we show that the general criteria for KMS states can be…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…
We analyse special classes of biorthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with $\mathcal{G}$- quasi bases. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly…
The Markov property entails the conditional independence structure inherent in Gibbs distributions for general classical Hamiltonians, a feature that plays a crucial role in inference, mixing time analysis, and algorithm design. However,…
We propose a generalization of Heisenberg picture quantum mechanics in which a Lagrangian and Hamiltonian dynamics is formulated directly for dynamical systems on a manifold with non--commuting coordinates, which act as operators on an…
We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by…