Related papers: A correspondence from renormalized frequency to he…
For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
We propose a new simple way to evaluate the effect of anharmonicity on a system's thermodynamic functions such as heat capacity. In this approach, the contribution of all potentially complicated anharmonic effects to constant-volume heat…
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…
It is widely believed that the underlying reality behind statistical mechanics is a deterministic and unitary time evolution of a many-particle wave function, even though this is in conflict with the irreversible, stochastic nature of…
An analytical model of high frequency oscillations of the kinetic and potential energies in a one-dimensional harmonic crystal with a substrate potential is obtained by introducing the nonlocal energies [1]. A generalization of the kinetic…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle…
Thermodynamic quantities, like heat, entropy, or work, are random variables, in stochastic systems. Here, we investigate the statistics of the heat exchanged by a Brownian particle subjected to a logarithm-harmonic potential. We derive…
Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of $|x|^\nu$ ($\nu>0$) type energies…
The statistical mechanical description of small systems staying in thermal equilibrium with an environment can be achieved by means of the Hamiltonian of mean force. In contrast to the reduced density matrix of an open quantum system, or…
Quantum statistical mechanics is formulated as an integral over classical phase space. Some details of the commutation function for averages are discussed, as is the factorization of the symmetrization function used for the grand potential…
In the context of quantum fields in time dependent classical backgrounds, we notice that the number of created particles with a given momentum largely deviates about its mean value. Guided with this observation we use a complete orthonormal…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
The composition of the quantum potential and its role in the breakdown of classical symplectic symmetry in quantum mechanics is investigated. General expressions are derived for the quantum potential in both configuration space and momentum…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…
In calorimetry and particularly in heat capacity measurements, different characteristic relaxation time constants may perturb the experiment which cannot be considered at thermodynamic equilibrium. In this case, thermodynamics of…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
This paper gives a simple derivation of the well-known expression of the frequency dependent complex heat capacity in modulated temperature experiments. It aims at clarified again that the generalized calorimetric susceptibility is only due…