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Journal of Physics Conference Series

Standard Reference for Zero Temperature from Quantum Supersymmetry is Possible?

C Marques, G S Dias, Helder Hipólito Chávez Sánchez

Published Jul 1, 2019• 0 citations
Publisher

Abstract

Abstract Supersymmetry at a susy harmonic oscillator, H(ω 1, ω 1), can be broken or restored in certain conditions and parameters, that are linked with thermal interaction and with a polynomial interactions of creation and annihilation operators. All possibles supersymmetric harmonic oscillators represented by a point (ω 1, ω 1) in the frequency space of the system, are in a two dimensional surface parametrized by the (ω 2, α 2), which we call s-surface, where α 2 is the interaction parameter. The temperature in the s-surface are intended to be zero. Interaction with the thermal bath represented by the tilde Hilbert space from the doubling Hilbert space, establishes thermal oscillations that push the system from the s-surface. In such a way we can define the set of all supersymmetric harmonic oscillator or in a equivalent way the s-surface as a global standard reference for zero temperature.

DOI
10.1088/1742-6596/1291/1/012035

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Abstract Supersymmetry at a susy harmonic oscillator, H(ω 1, ω 1), can be broken or restored in certain conditions and parameters, that are linked with thermal interaction and with a polynomial interactions of creation and annihilation operators. All possibles supersymmetric harmonic oscillators represented by a point (ω 1, ω 1) in the frequency space of the system, are in a two dimensional surface parametrized by the (ω 2, α 2), which we call s-surface, where α 2 is the interaction parameter. The temperature in the s-surface are intended to be zero. Interaction with the thermal bath represented by the tilde Hilbert space from the doubling Hilbert space, establishes thermal oscillations that push the system from the s-surface. In such a way we can define the set of all supersymmetric harmonic oscillator or in a equivalent way the s-surface as a global standard reference for zero temperature.
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Abstract This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.
Some years ago, one of the authors (MM) revived a concept to which he gave the name single-particle Dirac oscillator, while another of the authors (CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency omega . By considering the latter together with its partner corresponding to the replacement of omega by - omega , we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.
We consider a quantum system on the real line obeying a deformed Heisenberg algebra originally proposed by Wigner in 1950. Its explicit coordinate representation was provided by Yang in 1951 and in essence is identical in form with Dunkl's difference-differential operator introduced in 1989 in connection with roots systems of refection groups. Under certain conditions such quantum systems exhibit a supersymmetric (SUSY) structure where the reflection operator acts as the grading operator. We present a generalisation of Yang's representation by first considering only of one the two equations of motion in phase space. The corresponding non-interacting system is found to represent Witten's model of SUSY quantum mechanics. Imposing also the second equation of motion the original result of Wigner and Yang is reconsidered by extending their discussion to general symmetric potentials on the real line. As explicit example we discuss the harmonic oscillator and an attractive Coulomb-like potential V(x)=−γ/∣x∣V(x)=-γ/|x|V(x)=−γ/∣x∣. We also establish a Hooke-Newton duality between this Coulomb-like system and the original Wigner-Yang harmonic oscillator system.
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency~\\omega. By considering the latter together with its partner corresponding to the replacement of~\\omega by~-\\omega we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.