Nonrelativistic Quantum Systems Research Articles

Quantum soft waveguides with resonances induced by broken symmetry

We consider two-dimensional, non-relativistic quantum system with asymptotically straight soft waveguide. We show that the local deformation of the symmetric waveguide can lead to the emerging of the embedded eigenvalues living in the continuous spectrum. The main problem of this paper is devoted to the analysis of weak perturbation of the symmetric system. We show that the original embedded eigenvalues turn to the second sheet of the resolvent analytic continuation and constitute resonances. We describe the asymptotics of the real and imaginary components of the complex resonant pole depending on deformation. Finally, we generalize the problem to three dimensional system equipped with a soft layer.

Lorentz Symmetry Violation Effects Caused by the Coupling between the Field fμγ5 and the Derivative of the Fermionic Field on One-Dimensional Potentials

In search of physics beyond the standard model, new phenomena can be relevant in low energies. In view of the Standard Model Extension is an effective field theory, in this study we explore the fermionic sector by showing that the properties of nonrelativistic quantum systems can be modified. We study one-dimensional nonrelativistic quantum systems under Lorentz symmetry violation effects caused by the coupling between the fixed vector field fμγ5 and the derivative of the fermionic field. We deal with the quantum bouncer, the attractive inverse-square potential, a modified attractive inverse-square potential, and a scalar exponential potential inside this scenario of the Lorentz symmetry violation. Then, we show that the spectra of energy are influenced by the Lorentz symmetry violation effects.

Rotational and inverse-square potential effects on harmonic oscillator confined by flux field in a space–time with screw dislocation

This research paper delves into the study of a nonrelativistic quantum system, considering the interplay of noninertial effects induced by a rotating frame and confinement by the Aharonov–Bohm (AB) flux field with potential in the backdrop of topological defects, specifically a screw dislocation. We first focus on the harmonic oscillator problem, incorporating an inverse-square repulsive potential. Notably, it becomes evident that the energy eigenvalues and wave functions are intricately influenced by multiple factors: the topological defect parameter [Formula: see text] (representing the screw dislocation), the presence of a rotating frame engaged in constant angular motion with speed [Formula: see text] and the external potential. Then we study the quantum behavior of nonrelativistic particles, engaging in interactions governed by an inverse-square potential, all while taking into account the effects of the rotating frame. In both scenarios, a significant observation is made: the quantum flux field’s existence brings about a shift in the energy spectrum. This phenomenon bears a resemblance to the electromagnetic Aharonov–Bohm effect.

Thermodynamic properties and superstatistics analysis of particle in the non-relativistic system under the influence of trigonometric scarf potential using Dong proper quantization

There has been an intense study on the eigenvalue and eigenfunction of the nonrelativistic quantum system. The Schrodinger equation is important in the nonrelativistic quantum system that is used to analyze the quantum information of the system, so it attached the interest of the researchers to conduct the exploration on it. In most of the studies, the researchers expand the study of the solution of the Schrodinger equation to the physical properties of the system. The thermodynamical property is one of the physical properties and key to analyzing the characteristic of materials. It needs more investigation since it has the potential to form a new design of the material. In this study, the Schrodinger equation with trigonometric Scarf potential was solved using the Supersymmetry WKB quantization condition scheme, where the variable of trigonometric Scarf potential was transformed into the Poschl-Teller potential. The energy spectra were obtained by comparing the constant parameters between Trigonometric Scarf potential and Poschl-Teller potential and by using Dong proper quantization condition of transformed Supersymmetry WKB for trigonometric Scarf potential. The result shows that the energy spectra are influenced by the radial quantum number and the potential width, and the energy increase by the increase of the radial quantum number and the potential width. The thermodynamic properties of the system were obtained approximately using the energy spectra equation and were expressed in the erf function. The superstatistics mechanics was approximately obtained by using modified Delta Dirac function distribution for the Boltzmann factor. These properties are important to analyze the characteristic of the designed solids.

Gravitational entanglement and the mass contribution of internal energy in nonrelativistic quantum systems

Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise, post-Newtonian gravitational effects in composite nonrelativistic quantum systems have been discussed, where the internal energy contributes to the mass, promoting the mass to a Hilbert space operator. Employing a modified version of a previously considered thought experiment, it can be shown that both concepts, when combined, result in inconsistencies, reinforcing the arguments for the necessity of a rigorous derivation of the nonrelativistic limit of gravitating quantum matter from first principles.

Is there a relativistic Gorini-Kossakowski-Lindblad-Sudarshan master equation?

The celebrated GKLS master equation, widely called just Lindblad equation, is the universal dynamical equation of non-relativistic open quantum systems in their Markovian approximation. It is not necessary and perhaps impossible that GKLS equations possess sensible relativistic forms. In a lucid talk on black hole information loss paradox, David Poulin conjectured a Lorentz invariant GKLS master equation. It remained unpublished. Poulin passed away at heights of his activity. But the equation is really puzzling. A closer look uncovers a smartly hidden defect which leaves us without Lorentz invariant Markovian master equations. They, in view of the present author, should not exist.

Localized nonrelativistic quantum systems in curved spacetimes: A general characterization of particle detector models

In this manuscript we provide a consistent way of describing a localized non-relativistic quantum system undergoing a timelike trajectory in a background curved spacetime. Namely, using Fermi normal coordinates, we identify an inner product and canonically conjugate position and momentum operators defined in the rest space of the trajectory for each value of its proper time. This framework then naturally provides a recipe for mapping a quantum theory defined in a non-relativistic background to a theory around a timelike trajectory in curved spacetimes. This is done by reinterpreting the position and momentum operators and by introducing a local redshift factor to the Hamiltonian, which gives rise to new dynamics due to the curvature of spacetime and the acceleration of the trajectory. We then apply our formalism to particle detector models, that is, to the case where the non-relativistic quantum system is coupled to a quantum field in a curved background. This allows one to write a general definition for particle detector models which is able to recover the previous models in the literature. Our framework also allows one to estimate the regime of validity of these models, characterizing the situations where particle detectors can be used to accurately probe quantum fields.

Dephasing effects on the low-energy dynamics of ϕ4-model

In this paper, we investigate the Lindblad dynamics arising due to single particle loss and local dephasing in a d-dimensional nonrelativistic quantum system. Using Schwinger–Keldysh functional techniques, we derive the static mean field equation for the symmetry broken phase. Fluctuations over mean field are studied within the Bogoliubov approximation, and the momentum distribution and effective temperature are calculated. An effective temperature arises which depends on the dephasing rate [Formula: see text] and mean field particle density. Furthermore, a perturbative renormalization group (RG) upto one loop order is used to study the underlying dynamics of the model. The conditions for the system to be perturbative are obtained.

Quantum signatures of chaos in relativistic quantum billiards with shapes of circle- and ellipse-sectors* *Dedicated to the memory of Fritz Haake. Fritz introduced me (Barbara) into the field of quantum chaos. He supervised my diploma and doctoral thesis and since then has been a mentor, friend and helpful advisor during all the stages of my scientific career. I take his

According to the Berry–Tabor conjecture, the spectral properties of typical nonrelativistic quantum systems with an integrable classical counterpart agree with those of Poissonian random numbers. We investigate to what extend it applies to relativistic neutrino billiards (NBs) consisting of a spin-1/2 particle confined to a bounded planar domain by imposing suitable boundary conditions (BCs). In distinction to nonrelativistic quantum billiards (QBs), NBs do not have a well-defined classical counterpart. However, the peaks in the length spectra, that is, the modulus of the Fourier transform of the spectral density from wave number to length, of NBs are just like for QBs at the lengths of periodic orbits of the classical billiard (CB). This implies that there must be a connection between NBs and the dynamic of the CB. We demonstrate that NBs with shapes of circle- and ellipse-sectors with an integrable classical dynamic, obtained by cutting the circle and ellipse NB along symmetry lines, have no common eigenstates with the latter and that, indeed, their spectral properties can be similar to those of classically chaotic QBs. These features orginate from the intermingling of symmetries of the spinor components and the discontinuity in the BCs leading to contradictory conditional equations at corners connecting curved and straight boundary parts. To corroborate the necessity of the curved boundary part in order to generate GOE-like behavior, we furthermore consider the right-angled triangle NB constructed by halving the equilateral-triangle NB along a symmetry axis. For an understanding of these findings in terms of purely classical quantities we use the semiclassical approach recently developed for massive NBs, and Poincaré–Husimi distributions of the eigenstates in classical phase space. The results indicate, that in the ultrarelativistic limit these NBs do not show the behavior expected for classically chaotic QBs.

Time reversal symmetry for classical, non-relativistic quantum and spin systems in presence of magnetic fields

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are non-relativistic, and are described by the Schrödinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These results are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations.

Phase and group velocities for correlation spreading in the Mott phase of the Bose-Hubbard model in dimensions greater than one

Lieb-Robinson and related bounds set an upper limit on the speed at which information propagates in nonrelativistic quantum systems. Experimentally, light-cone-like spreading has been observed for correlations in the Bose-Hubbard model (BHM) after a quantum quench. Using a two-particle irreducible (2PI) strong-coupling approach to out-of-equilibrium dynamics in the BHM we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two, and three dimensions as a function of interaction strength. Our results are in quantitative agreement with measurements of the speed of spreading of single-particle correlations in both the one- and two-dimensional BHM realized with ultracold atoms. They also are consistent with the claim that the phase velocity rather than the group velocity was observed in recent experiments in two dimensions. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and explore how the anisotropy in the velocity varies across the phase diagram of the BHM. Our results establish the 2PI strong-coupling approach as a powerful tool to study out-of-equilibrium dynamics in the BHM in dimensions greater than one.

Discrete self-adjointness and quantum dynamics. Travel times

We use a discrete derivative to introduce a time operator for non-relativistic quantum systems with point spectrum. The symmetry requirement on the time operator leads to well-defined time values related to the dynamics of discrete quantum systems. As an illustration, we find travel times between hits with the walls for the quantum particle in a box model. These times suggest a classical analog of time eigenstates. We also briefly consider the Woods–Saxon potential and propose classical analogs for it.

Lieb-Robinson bounds and out-of-time order correlators in a long-range spin chain

Lieb Robinson bounds quantify the maximal speed of information spreading in nonrelativistic quantum systems. We discuss the relation of Lieb Robinson bounds to out of time order correlators, which correspond to different norms of commutators $C(r,t) = [A_i(t),B_{i+r}]$ of local operators. Using an exact Krylov space time evolution technique, we calculate these two different norms of such commutators for the spin 1/2 Heisenberg chain with interactions decaying as a power law $1/r^\alpha$ with distance $r$. Our numerical analysis shows that both norms (operator norm and normalized Frobenius norm) exhibit the same asymptotic behavior, namely a linear growth in time at short times and a power law decay in space at long distance, leading asymptotically to power law light cones for $\alpha<1$ and to linear light cones for $\alpha>1$. The asymptotic form of the tails of $C(r,t)\propto t/r^\alpha$ is described by short time perturbation theory which is valid at short times and long distances.

Lorentz violation induced by Rashba coupling via non-commutative geometry

In this paper we consider a simple non-relativistic quantum system for a particle confined inside a pseudo-harmonic oscillator potential in the non-commutative space. We study the influence of non-commutative background on the energy spectrum of the particle by considering the Rashba spin-orbit interaction. We show that the Rashba interaction can generate the Lorentz violation effect in the non-commutative background, which is independent of potential. Finally, we find a compatible bound on the Lorentz violation parameter of electrons as an order of in the non-relativistic system.

Particle detectors as witnesses for quantum gravity

We present a model for the coupling of non-relativistic quantum systems with a linearized gravitational field from a Lagrangian formulation. The coupling strongly resembles the light-matter interaction models that are known to be well approximated by the Unruh-DeWitt detector model for interactions with quantum fields. We then apply our model to linearized quantum gravity, which allows us to propose a detector based setup that can in principle probe the quantum nature of the gravitational field.

Manifestations of chaos in relativistic quantum systems - A study based on out-of-time-order correlator

Previous work in the field of relativistic quantum chaos has revealed initial evidence that the manifestations of classical chaos in relativistic quantum systems tend to be weakened as compared with those in nonrelativistic quantum systems. To place this finding on a firmer ground, we investigate the relativistic quantum fingerprints of classical chaos using the out-of-time-order correlator (OTOC). OTOC has recently been applied to a number of fields in physics and it holds special promises for the field of quantum chaos, but existing work focused exclusively on nonrelativistic quantum systems. Calculating and analyzing OTOC for relativistic quantum billiard systems described by the massless Dirac equation, we find that the signatures of classical chaos are indeed characteristically less pronounced in relativistic than in nonrelativistic quantum systems. The finding is substantiated by studying four different aspects of OTOC. Firstly, in the energy eigenspace, in the short time regime there is a complete lack of any signature of chaos associated with the evolution of OTOC in the Dirac billiard due to the relativistic quantum phenomenon of Zitterbewegung, in contrast to nonrelativistic quantum billiard systems where chaos leaves behind a quite distinct signature. Secondly, weakening of the relativistic quantum manifestations of classical chaos occurs in the long time regime as well. Thirdly, evolution of the wave packet based OTOC also reveals that the fingerprints of chaos are much less pronounced in the Dirac billiard systems as compared with the Schrödinger billiards. Fourthly, the level spacing statistics of the OTOC operators in systems with classically integrable and chaotic dynamics, which are characteristically distinct in the Schrödinger billiards, bear a strong similarity in the Dirac billiards, indicating again the dwindling effects of chaos. The OTOC based results suggest that the impacts of classical chaos are generally weaker in relativistic than in nonrelativistic quantum systems, a fundamental issue that warrants further investigation.

Diffeomorphism Group Representations in Nonrelativistic and Relativistic Quantum Theory: Some Future Directions

Diffeomorphism groups and their unitary representations unify the description of a wide variety of diverse nonrelativistic (Galilean) quantum systems. In recent work, we have suggested an approach to relativistic quantum field theory that begins with hierarchies of diffeomorphism group representations and the corresponding current densities. We introduce (noncovariant) creation and annihilation fields that intertwine the representations, and restore the (relativistic) spacetime symmetry by redefining local quantum fields and the Hamiltonian operator in terms of the intertwining fields and current densities. Here we outline the main ideas, and point to next steps and possible future directions of this line of inquiry.

Emergent locality in systems with power-law interactions

Locality imposes stringent constraints on the spreading of information in nonrelativistic quantum systems, which is reminiscent of a "light-cone," a casual structure arising in their relativistic counterparts. Long-range interactions can potentially soften such constraints, allowing almost instantaneous long jumps of particles, thus defying causality. Since interactions decaying as a power-law with distance, $r^{-\alpha}$, are ubiquitous in nature, it is pertinent to understand what is the fate of causality and information spreading in such systems. Using a numerically exact technique we address these questions by studying the out-of-time-order correlation function of a representative generic system in one-dimension. We show that while the interactions are long-range, their effect on information spreading is asymptotically negligible as long as $\alpha>1$. In this range we find a complex compound behavior, where after a short transient a fully local behavior emerges, yielding asymptotic "light-cones" virtually indistinguishable from "light-cones" in corresponding local models. The long-range nature of the interaction is only expressed in the power-law leaking of information from the "light-cone," with the same exponent as the exponent of the interaction, $\alpha$. Our results directly imply that all previously obtained rigorous bounds on information spreading in long-range interacting systems are not tight, and thus could be improved.

Locality and Digital Quantum Simulation of Power-Law Interactions.

The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS’18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α > 3D (where D is the number of dimensions).

Partitioned density matrices and entanglement correlators

The density matrix of a non-relativistic quantum system, divided into $N$ sub-systems, is rewritten in terms of the set of all partitioned density matrices for the system. For the case where the different sub-systems are distinguishable, we derive a hierarchy of equations of motion linking the dynamics of all the partitioned density matrices, analogous to the "Schwinger-Dyson" hierarchy in quantum field theory. The special case of a set of $N$ coupled spin-$1/2$ "qubits" is worked out in detail. The equations are then rewritten in terms of a set of "entanglement correlators", which comprise all the possible correlation functions for the system - this case is worked out for coupled spin systems. The equations of motion for these correlators can be written in terms of a first-order differential equation for an entanglement correlator supervector.