Related papers: On the Harmonic Oscillator Regularization of Parti…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called…
Simple calculations indicate that the partition function for a black hole is defined only if the temperature is fixed on a finite boundary. Consequences of this result are discussed. (Contribution to the Proceedings of the Lanczos Centenary…
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
Quantum mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle…
A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to…
Quantization of the damped harmonic oscillator is taken as leitmotiv to gently introduce elements of quantum probability theory for physicists. To this end, we take (graduate) students in physics as entry level and explain the physical…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
In this paper, we study the statistical mechanics within the polymer quantization framework in the semiclassical regime. We apply a non-canonical transformation to the phase space variables. Then, we use this non-canonical transformation to…
For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational…
In this paper, we obtain upper and lower bounds for the partition function $p(n)$ by using an elementary geometric inequality in Euclidean space, and we extend the method to generalizations of the partition function.
We calculate the quantum statistical force acting on a partition wall that divides a one dimensional box into two halves. The two half boxes contain the same (fixed) number of noninteracting bosons, are kept at the same temperature, and…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
Does bound entanglement naturally appear in quantum many-body systems? We address this question by showing the existence of bound-entangled thermal states for harmonic oscillator systems consisting of an arbitrary number of particles. By…