Supersymmetric Quantum Research Articles

High-order SUSY-QM, the quantum XP model and zeroes of the Riemann Zeta function

Abstract Making use of the first- and second-order algorithms of supersymmetric quantum mechanics (SUSY-QM), we construct quantum mechanical Hamiltonians whose spectra are related to the zeroes of the Riemann Zeta function ζ(s). Inspired by the model of Das and Kalauni (DK) A Das and P Kalauni (2019 Physics Letters B 791, 265-269) which corresponds to this function in the strip 0 < Re [ s ] < 1 , and taking the factorization energy equal to zero, we use the wave function ∣x∣−S , S ∈ C , as a seed solution for our algorithms, obtaining XP-like operators. Thus, we construct SUSY-QM partner Hamiltonians whose zero energy mode locates exactly the nontrivial zeroes of ζ(s) along the critical line Re [ s ] = 1 / 2 in the complex plane. We further find that unlike the DK case, where the SUSY-QM partner potentials correspond to free particles, our partner potentials belong to the family of inverse squared distance potentials with complex couplings.

Study on Kalb–Ramond field localization in f(T) gravity theory with a noncanonical scalar field

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of [Formula: see text] gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the [Formula: see text] branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential.

Supersymmetric quantum potentials analogs of classical electrostatic fields

A relation between classical electrostatic fields and Shrödinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the electrostatic potential as the natural logarithm of a nodeless function, it is demonstrated that the electrostatic fields fulfil the Bernoulli equation associated to a second-order confluent supersymmetric transformation. By using the so-called confluent algorithm, it is possible, given a charge density, to find the corresponding electrostatic field as well as the supersymmetric potentials. Furthermore, the associated charge density and the electrostatic field profile of Schrödinger-like solvable potentials can be determined.

Resonance Energy and Wavefunction of $${}^{{31}}$$Ne: a Calculation Using Supersymmetric Quantum Mechanics

Resonance Energy and Wavefunction of $${}^{{31}}$$Ne: a Calculation Using Supersymmetric Quantum Mechanics

Supersymmetric quantum mechanics, multiphoton algebras and coherent states

The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and creation operators, as well as by Hamiltonians which are functions of an appropriate number operator. The algebras obtained turn out to be polynomial deformations of the corresponding single-photon algebra previously studied in literature. The Barut-Girardello coherent states, which are eigenstates of the annihilation operator, are obtained and their uncertainty relations are explored by means of the associated quadratures.

Time-domain supersymmetry for massless scalar and electromagnetic fields in anisotropic cosmologies

It is shown that any cosmological anisotropic model produces supersymmetric theories for both massless scalar and electromagnetic (abelian) fields. This supersymmetric theory is the time-domain analogue of a supersymmetric quantum mechanics algebra theory. In this case, the variations of the anisotropic scale factors of the Universe are responsible for triggering the supersymmetry. For scalar fields, the superpartner fields evolve in two different cosmological scenarios (Universes). On the other hand, for propagating electromagnetic fields, supersymmetry is manifested through its polarization degrees of freedom in one Universe. In this case, polarization degrees of freedom of electromagnetic waves, which are orthogonal to its propagation direction, become superpartners from each other. This behavior can be measured, for example, through the rotation of the plane of polarization of cosmological light.

Supersymmetric quantum mechanics and the Riemann hypothesis

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the vanishing ground state energies in this model. The model provides a natural form of supersymmetry.

Feynman diagrams in four-dimensional holomorphic theories and the Operatope

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

New AdS2/CFT1 pairs from AdS3 and monopole bubbling

We present general results on generating AdS2 solutions to Type II supergravity from AdS3 solutions via U(1) and SL(2) T-dualities. We focus on a class of Type IIB solutions with small \U0001d4a9 = 4 supersymmetry, that we show can be embedded into a more general class of solutions obtained by double analytical continuation from AdS3 geometries with small \U0001d4a9 = (0, 4) supersymmetry constructed in the literature. We then start the analysis of the superconformal quantum mechanics dual to the \U0001d4a9 = 4 backgrounds focusing on a subclass of AdS2 × S3 × \U0001d54b3 solutions foliated over a Riemann surface. We show that the associated supersymmetric quantum mechanics describes monopole bubbling in 4d \U0001d4a9 = 2 supersymmetric gauge theories living in D3-D7 branes, as previously discussed in the literature. Therefore, we propose that our solutions provide a geometrical description via holography of monopole bubbling in 4d \U0001d4a9 = 2 SCFTs. We check our proposal with the computation of the central charge.

Quantum Hamilton–Jacobi quantization and shape invariance

Quantum Hamilton–Jacobi (QHJ) quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known conventional potentials. Using a recent work in supersymmetric quantum mechanics, we prove that the additive shape invariance of all conventional potentials and unbroken supersymmetry are sufficient conditions for their solvability within the QHJ formalism.

Variational eigenfunctions for excited states inspired by supersymmetric quantum mechanics and the Gram–Schmidt process

Factorization methods such as the Hamiltonian hierarchy have been useful to find eigenfunctions for Schrödinger equations, in particular, for potentials that are partially or approximately solvable. In this paper, an alternative approach is proposed to study excited states via the variational method. The trial functions are built from the exact or approximate superpotential for the ground state combined with the Gram–Schmidt process to ensure orthogonalization between the functions. The results found variationally for one dimensional potentials are compared with previous results from the literature. The energy eigenvalues obtained agree with previous ones and, for most of the results, the percentage difference between the proposed approach and others in the literature is less than 0.1%. The method introduced is an effective and intuitive approach to determine trial wave functions for the excited states. This approach can be useful in studying the Schrödinger equation and related problems which can be mapped onto a Schrödinger type-equation as, for example, the Fokker–Planck equation.

The Dirac equation with /non--symmetric potentials in curved spacetime backgrounds

In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational static background in the presence of /non--symmetric potential interactions. The exponential metric component have formed the reduced Dirac operator into the general supersymmetric model within mass changing with coordinates. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) using Lie algebras and the supersymmetric quantum mechanical approaches. Moreover, after obtaining a general Sturm-Liouville type equation using a convenient mapping, the system have become available to be investigated within η- pseudo-Hermiticity. With this context, η operator is found for the examples of complex trigonometric Rosen-Morse potential and complex Morse potentials with real and complex parameters of the initial system and finally the solutions are obtained for each model with the graphics of energy values and probability densities.

Magnetic charge and black hole supersymmetric quantum statistical relation

Magnetic charge and black hole supersymmetric quantum statistical relation

Two-loop superfield effective potential for N=2 , d=3 supersymmetric quantum electrodynamics with higher derivatives

In the $\mathcal{N}=2$, $d=3$ superspace, we consider a higher-derivative generalization of the supersymmetric quantum electrodynamics, where the higher-derivative operator is a polynomial function of the d'Alembertian with arbitrary degree. For this theory, we use the background field quantization in a higher-derivative $R_\xi$ gauge to explicitly calculate the superfield effective potential up to two loops in the K\"{a}llerian approximation. This superfield effective potential is obtained in a closed form and in terms of elementary functions.

Supersymmetric quantum mechanical system for locating the Riemann zeros

Supersymmetric quantum mechanical system for locating the Riemann zeros

Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and via explicit large deviations at various levels

For boundary-driven non-equilibrium Markov models of non-interacting particles in one dimension, either in continuous space with the Fokker–Planck dynamics involving an arbitrary force F(x) and an arbitrary diffusion coefficient D(x), or in discrete space with the Markov jump dynamics involving arbitrary nearest-neighbor transition rates , the Markov generator can be transformed via an appropriate similarity transformation into a quantum supersymmetric Hamiltonian with many remarkable properties. We first describe how the mapping from the boundary-driven non-equilibrium dynamics towards some dual equilibrium dynamics (see Tailleur et al 2008 J. Phys. A: Math. Theor. 41 505001) can be reinterpreted via the two corresponding quantum Hamiltonians that are supersymmetric partners of each other, with the same energy spectra. We describe the consequences for the spectral decomposition of the boundary-driven dynamics, and we give explicit expressions for the Kemeny times needed to converge towards the non-equilibrium steady states. We then focus on the large deviations at various levels for empirical time-averaged observables over a large time-window T. We start with the always explicit Level 2.5 concerning the joint distribution of the empirical density and of the empirical flows before considering the contractions towards lower levels. In particular, the rate function for the empirical current alone can be explicitly computed via the contraction from the Level 2.5 using the properties of the associated quantum supersymmetric Hamiltonians.

Thermomagnetic properties and its effects on Fisher entropy with Schioberg plus Manning-Rosen potential (SPMRP) using Nikiforov-Uvarov functional analysis (NUFA) and supersymmetric quantum mechanics (SUSYQM) methods

Thermomagnetic properties, and its effects on Fisher information entropy with Schioberg plus Manning-Rosen potential are studied using NUFA and SUSYQM methods in the presence of the Greene-Aldrich approximation scheme to the centrifugal term. The wave function obtained was used to study Fisher information both in position and momentum spaces for different quantum states by the gamma function and digamma polynomials. The energy equation obtained in a closed form was used to deduce numerical energy spectra, partition function, and other thermomagnetic properties. The results show that with an application of AB and magnetic fields, the numerical energy eigenvalues for different magnetic quantum spins decrease as the quantum state increases and completely removes the degeneracy of the energy spectra. Also, the numerical computation of Fisher information satisfies Fisher information inequality products, indicating that the particles are more localized in the presence of external fields than in their absence, and the trend shows complete localization of quantum mechanical particles in all quantum states. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. Our potential reduces to Schioberg and Manning-Rosen potentials as special cases. The energy equations obtained from the NUFA and SUSYQM were the same, demonstrating a high level of mathematical precision.

Magnon dynamics in a skyrmion-textured domain wall of antiferromagnets

We theoretically investigate the interaction between magnons and a Skyrmion-textured domain wall in a two-dimensional antiferromagnet and elucidate the resultant properties of magnon transport. Using supersymmetric quantum mechanics, we solve the scattering problem of magnons on top of the domain wall and obtain the exact solutions of propagating and bound magnon modes. Then, we find their properties of reflection and refraction in the Skyrmion-textured domain wall, where magnons experience an emergent magnetic field due to its non-trivial spin texture-induced effective gauge field. Based on the obtained scattering properties of magnons and the domain wall, we show that the thermal transport decreases as the domain wall's chirality increases. Our results suggest that the thermal transport of an antiferromagnet is tunable by modulating the Skyrmion charge density of the domain wall, which might be useful for realizing electrically tunable spin caloritronic devices.

Generalized Langer correction and the exactness of WKB for all conventional potentials

In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it generates the exact quantization condition for all conventional potentials. We also prove that this correction is related to the previously proven exactness of SWKB for these potentials.

Non-linear Schrödinger equation with time-dependent balanced loss-gain and space–time modulated non-linear interaction

We consider a class of one dimensional vector Non-linear Schrödinger Equation (NLSE) in an external complex potential with Balanced Loss-Gain (BLG) and Linear Coupling (LC) among the components of the Schrödinger field. The solvability of the generic system is investigated for various combinations of time modulated LC and BLG terms, space–time dependent strength of the nonlinear interaction and complex potential. We use a non-unitary transformation followed by a reformulation of the differential equation in a new coordinate system to map the NLSE to solvable equations. Several physically motivated examples of exactly solvable systems are presented for various combinations of LC and BLG, external complex potential and nonlinear interaction. Exact localized nonlinear modes with spatially constant phase may be obtained for any real potential for which the corresponding linear Schrödinger equation is solvable. A method based on supersymmetric quantum mechanics is devised to construct exact localized nonlinear modes for a class of complex potentials. The real superpotential corresponding to any exactly solved linear Schrödinger equation may be used to find a complex-potential for which exact localized nonlinear modes for the NLSE can be obtained. The solutions with singular phases are obtained for a few complex potentials.