Related papers: Schwinger's SUSY Oscillators: An Analysis
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called $\phi$-theory in $d+1$…
We attempt to build systematically the low-energy effective Lagrangian for the Einstein--Cartan formulation of gravity theory that generally includes the torsion field. We list all invariant action terms in certain given order; some of the…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
The Schwinger model with two massive fermions is a nontrivial theory for which no analytical solution is known. The strong coupling limit of the theory allows for different semiclassical approximations to extract properties of its low-lying…
In this manuscript we consider the transformations of the oscillators of the bosonic fields of the superstring in terms of the fermions oscillators and vice versa. We demand the exchange of the commutation and anti-commutation relations of…
The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show…
We study a model of quantum mechanical fermions with matrix-like index structure (with indices $N$ and $L$) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with $q$-deformed…
Evolution of occupation number is studied for a bosonic oscillator (with one and two degrees of freedom) linearly fully coupled to fermionic and bosonic heat baths. The lack of equilibrium in this oscillator is discussed in the light of the…
We study the thermodynamics of quantum particles with long-range interactions at T=0. Specifically, we generalize the Hamiltonian Mean Field (HMF) model to the case of fermions and bosons. In the case of fermions, we consider the…
A new kind of fundamental superfield is proposed, with an Ising-like Euclidean action. Near the Planck energy it undergoes its first stage of symmetry-breaking, and the ordered phase is assumed to support specific kinds of topological…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in…
The conservation law for the orbital plus spin angular momentum of a free Dirac particle in curved spacetime requires that the affine connection has the antisymmetric part: the torsion tensor, which extends general relativity to the…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bi-spinor quantum fields, which are the expansion coefficients of the forms in the bi-spinor basis of Becher and Joos [7]. The canonical…
We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and…