Related papers: On the Harmonic Oscillator Regularization of Parti…
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…
It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed…
We study a harmonic molecule confined to a one--dimensional box with impenetrable walls. We explicitly consider the symmetry of the problem for the cases of different and equal masses. We propose suitable variational functions and compare…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…
This paper exploits the connection between the quantum many-particle density of states and the partitioning of an integer in number theory. For $N$ bosons in a one dimensional harmonic oscillator potential, it is well known that the…
We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
By encoding a qudit in a harmonic oscillator and investigating the infinite limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators for…
We discuss the positional fluctuations of a quantum harmonic oscillator in a heat bath. Analytic expressions are given for the probability distribution functions of the oscillator position in general and limiting (classical and ground…
Quantum particle is considered confined in a toy-model potential possessing multiple minima. For the specific choice of the family of potentials (in the form of harmonic oscillator plus several logarithmic infinitely high but penetrable…
We describe a new model of massless thermal bosons which predicts an hyperbolic fluctuation spectrum at low frequencies. It is found that the partition function per mode is the Euler generating function for unrestricted partitions $p(n)$.…
The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral method which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The time…
Despite their simplicity, quantum harmonic oscillators are ubiquitous in the modeling of physical systems. They are able to capture universal properties that serve as reference for the more complex systems found in nature. In this spirit,…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
We use the partition functions on S^1 x S^n of various conformal field theories in four and six dimensions in the limit of vanishing coupling to study the high temperature thermodynamics. Certain modular properties exhibited by the…
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $V(x) = \frac{1}{2} \omega^2 x^2 + g x^4$ is presented. Using a path integral formalism, the exact…
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…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…