Related papers: Schr\"odinger and Planck oscillators: not quite th…
The problem of the initial conditions for the oscillator model of quantum dissipative systems is studied. It is argued that, even in the classical case, the hypothesis that the environment is in thermal equilibrium implies a statistical…
Small quantum systems non-weakly coupled to a bath become in the quantum regime surrounded by a cloud of photons or phonons, which modifies their thermodynamic behavior. Exactly solvable examples are the Brownian motion of a quantum…
The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb,…
A nonpolynomial one-dimensional quantum potential representing an oscillator, that can be considered as placed in the middle between the harmonic oscillator and the isotonic oscillator (harmonic oscillator with a centripetal barrier), is…
The interrelationship between the non-Markovian stochastic Schr\"odinger equations and the corresponding non-Markovian master equations is investigated in the finite temperature regimes. We show that the general finite temperature…
The metaphor of a clock in physics describes near-equilibrium reversible phenomena such as an oscillating spring. It is surprising that for chemical and biological clocks the focus has been exclusively on the far-from-equilibrium…
We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the…
Energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal…
We use the Lewis and Riesenfeld invariant method [\textit{J. Math. Phys.} \textbf{10}, 1458 (1969)] and a unitary transformation to obtain the exact Schr\"{o}dinger wave functions for time-dependent harmonic oscillators exhibiting…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
The thermodynamics of the discrete nonlinear Schr\"odinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a…
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulae for the microcanonical partition functions in the case of non-interacting massless neutral particles…
We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude.…
The quantum dynamics of a two-level system coupled to an Ohmic spin- bath is studied by means of the perturbation approach based on a unitary transformation. A scattering function $\xi_k$ is introduced in the transformation to take into…
A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schr\"odinger equation. For example, a free…
The equation of state of a system at equilibrium may be derived from the canonical or the grand canonical partition function. The former is a function of temperature T, while the latter also depends on the chemical potential \mu for…
This article examines the consequences of the existence of an upper particle momentum limit in quantum electrodynamics, where this momentum limit is the Planck momentum. The method used is Fourier analysis as developed already by Fermi in…
We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics…
Quantum nonclassicality is the basic building stone for the vast majority of quantum information applications and methods of its generation are at the forefront of research. One of the obstacles any method needs to clear is the looming…
We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase…