Related papers: Bernstein processes, Euclidean Quantum Mechanics a…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
We introduce the idea of weakly coherent collisional models, where the elements of an environment interacting with a system of interest are prepared in states that are approximately thermal, but have an amount of coherence proportional to a…
We derive quantum Boltzmann equations for preheating by means of the density matrix formalism, which account for both the non-adiabatic particle production and the leading collisional processes between the produced particles. In so doing,…
We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential…
In the framework of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan gravity with an action depending both of the Ricci scalar and the so-called Holst-invariant curvature we consider models that include cubic terms of the latter in the…
We consider thermal machines powered by locally equilibrium reservoirs that share classical or quantum correlations. The reservoirs are modelled by the so-called collisional model or repeated interactions model. In our framework, two…
By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate…
Starting from the Helmholtz free energy we calculate analytically first- and second-order derivatives, as internal energy and specific heats, for the ideal system and the exchange and correlation interactions covering a broad range of…
We illustrate recent results concerning the validity of the work fluctuation theorem in open quantum systems [M. Campisi, P. Talkner, and P. H\"{a}nggi, Phys. Rev. Lett. {\bf 102}, 210401 (2009)], by applying them to a solvable model of an…
Quantum thermodynamics addresses the emergence of thermodynamical laws from quantum mechanics. The link is based on the intimate connection of quantum thermodynamics with the theory of open quantum systems. Quantum mechanics inserts…
A review of computations of free energy for Gibbs states on stationary but not static gravitational and gauge backgrounds is given. On these backgrounds wave equations for free fields are reduced to eigen-value problems which depend…
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally…
We discuss an approach to determine averages of the work, dissipated heat and variation of internal energy of an open quantum system driven by an external classical field. These quantities are measured by coupling the quantum system to a…
We construct an integrable Hubbard model with impurity site containing spin and charge degrees of freedom. The Bethe ansatz equations for the Hamiltonian are derived and two alternative sets of equations for the thermodynamical properties.…
We discuss a formulation of exactly Poincar\'e invariant quantum mechanics where the input is model Euclidean Green functions or their generating functional. We discuss the structure of the models, the construction of the Hilbert space, the…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
The notion of temperature in many body elementary particle processes is in a common use for decades. Thermal models have become simple and universal effective tools to describe particle production -- not only in high energy heavy ion…
The procedure of nonperturbative quantization \`a la Heisenberg is considered. A few applications, features, perspectives, problems, and so on are considered. The comparison with turbulence modeling is performed.
Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process {\xi} with memory as e.g. a L\'evy semi-stationary process.…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this…