Related papers: The quantum canonical ensemble in phase space
The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…
The Weyl-Wigner representations for canonical thermal equilibrium quantum states are obtained for the whole class of quadratic Hamiltonians through a Wick rotation of the Weyl-Wigner symbols of Heisenberg and metaplectic operators. The…
The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuations theorems. Here we develop a semiclassical approximation to the work distribution for a quench process in chaotic…
It is known that ab initio molecular dynamics based on the electron ground state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temperature is low compared to the first electron eigenvalue gap.…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…
The nonzero ground-state energy of the quantum mechanical harmonic oscillator implies quantum fluctuations around the minimum of the potential with the mean square value proportional to Planck's constant. In classical mechanics thermal…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
The trace of an arbitrary product of quantum operators with the density operator is rendered as a multiple phase space integral of the product of their Weyl symbols with the Wigner function. Interspersing the factors with various evolution…
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical…
We study the nonequilibrium steady-state of a fully-coupled network of $N$ quantum harmonic oscillators, interacting with two thermal reservoirs. Given the long-range nature of the couplings, we consider two setups: one in which the number…
Thermalization in closed quantum systems can be explained either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum mechanical formalism such as spectral…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
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…
The classical boundaries of the quantum singular oscillator (SO) is addressed under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to comparatively evaluate phase-space and configuration space quantum trajectories as well as to…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
We formulate a canonical quantization of Equilibrium Thermodynamics by applying Dirac's theory of constrained systems. Thermodynamic variables are treated as conjugate pairs of coordinates and momenta, allowing extensive and intensive…
In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the…