Nonrelativistic Particle Research Articles

Diffraction in time of an entangled non-relativistic quantum particle

The diffraction process of an entangled non-relativistic quantum particle in time domain is investigated. The scenario consists of two entangled spin-0 particles and a quantum shutter, which is opened at an initial time. The particles are traveling in two opposite sides and expressed with a single wave function. The integral solution of the Schrödinger equation is considered for two particles case. The initial condition is expressed in terms of an entangled wave function. The time-diffracted matter wave is obtained in terms of the Fresnel integral. The effect of the phenomenon of diffraction in time is examined numerically for the entangled system of two particles.

Two-body bound states through Yukawa forces and perspectives on hydrogen and deuterium

We present and discuss numerical solutions to a two-body quantum bound state problem closely related to that of the hydrogen atom and the deuterium nucleus. The forces binding the particles of our system are Yukawa forces, which fall off with distance faster than the Coulomb force and arise for non-relativistic particles whose interactions are mediated by massive scalar or vector particles; the Coulomb force arises in the limit of massless mediators such as photons. We use the solutions to explain several features of deuterium. We also present heuristic estimates of ground state energies and energy level degeneracy breaking. Studying this Yukawa two-body system provides insights into hydrogen, deuterium, and two-body bound states, generally. We describe our undergraduate-accessible procedure for numerically solving non-relativistic two-body bound state problems with mathematica in the appendix.

Quantum State Evolution in an Environment of Cosmological Perturbations

We study the pure and thermal states of quantized scalar and tensor perturbations in various epochs of Universe evolution. We calculate the density matrix of non-relativistic particles in an environment of these perturbations. We show that particle’s motion can be described by a stochastic equation with a noise coming from the cosmological environment. We investigate the squeezing of Gaussian wave packets in different epochs and its impact on the noise of quantized cosmological perturbations.

Relativistic causality in particle detector models: Faster-than-light signaling and impossible measurements

We analyze potential violations of causality in Unruh DeWitt-type detector models in relativistic quantum information. We proceed by first studying the relation between faster-than-light signaling and the causal factorization of the dynamics for multiple detector-field interactions. We show in what way spatially extended non-relativistic detector models predict superluminal propagation of the field's initial conditions. We draw parallels between this characteristic of detector models, stemming from their non-relativistic dynamics, and Sorkin's "impossible measurements on quantum fields" arXiv:gr-qc/9302018. Based on these features, we discuss the validity of measurements in QFT when performed with non-relativistic particle detectors.

Nonlocal effects from boosted dark matter in indirect detection

Indirect dark matter (DM) detection typically involves the observation of standard model (SM) particles emerging from DM annihilation/decay inside regions of high dark matter concentration. We consider an annihilation scenario in which this reaction has to be initiated by one of the DMs involved being boosted while the other is an ambient non-relativistic particle. This "trigger" DM must be created, for example, in a previous annihilation or decay of a heavier component of DM. Remarkably, boosted DM annihilating into gamma-rays at a specific point in a galaxy could actually have traveled from its source at another point in the same galaxy or even from another galaxy. Such a "non-local" behavior leads to a non-trivial dependence of the resulting photon signal on the galactic halo parameters, such as DM density and core size, encoded in the so-called "astrophysical" $J$-factor. These non-local $J$-factors are strikingly different than the usual scenario. A distinctive aspect of this model is that the signal from dwarf galaxies relative to the Milky Way tends to be suppressed from the typical value to various degrees depending on their characteristics. This feature can thus potentially alleviate the mild tension between the DM annihilation explanation of the observed excess of $\sim$ GeV photons from the Milky Way's galactic center vs. the apparent non-observation of the corresponding signal from dwarf galaxies.

Testing dark matter interactions with CMB spectral distortions

Possible interactions of dark matter (DM) with Standard Model (SM) particles can be tested with spectral distortions (SDs) of the cosmic microwave background (CMB). In particular, a non-relativistic DM particle that scatters elastically with photons, electrons or nuclei imprints a negative chemical potential $\mu$ to the CMB spectrum. This article revisits the first study of this effect, with an accurate treatment of heat exchange between DM and SM particles. We show that the instantaneous-decoupling approximation made in the original study systematically and significantly underestimates the amplitude of SDs. As a consequence, we derive tighter upper bounds to the DM-SM elastic-scattering cross section for DM masses $m_\chi \lesssim 0.1$ MeV, from the non-detection of $\mu$-distortions by FIRAS. We also show that a future instrument like PIXIE, sensitive to $|\mu| \sim 10^{-8}$, would be able to probe DM-SM cross sections much smaller than first forecasted, and orders of magnitude below current upper limits from CMB-anisotropy data, up to DM masses of $\sim 1$ GeV. Lastly, we study the sensitivity of SDs to the electric and magnetic dipole moments of the DM. Although SDs can place non-trivial constraints on these models, we find that even future SD experiments are unlikely to improve upon the best current bounds. This article is accompanied by the public code DMDIST, which allows one to compute CMB SDs for generic particle-DM models, specified by their cross sections for elastic scattering with and annihilation into SM particles.

Sharing symmetries in non-linear systems: Generalized Heisenberg–Weyl algebra on the de Sitter space-time out of the sphere S3

In this paper, we exploit the formal equivalence of the Solution Manifold of two distinct physical systems to create enough symmetries so as to characterize them by Noether Invariants, thus favoring their future quantization. In so doing, we somehow generalize the Arnold Transformation for non-necessarily linear systems. Very particularly, this algorithm applies to the case of the motion on the de Sitter space-time providing a finite-dimensional algebra generalizing the Heisenberg–Weyl algebra globally. In this case, the basic (contact) symmetry is imported from the motion of a (non-relativistic) particle on the sphere [Formula: see text].

Quantum particle on dual root lattice in Weyl alcove

Classes of discrete quantum models that describe a free non-relativistic quantum particle propagating on rescaled and shifted dual root lattices inside closures of Weyl alcoves are constructed. Boundary conditions of the discrete quantum billiard systems on the borders of the Weyl alcoves are controlled by specific combinations of Dirichlet and Neumann walls that result from sign homomorphisms and admissible shifts inherent in generalized dual root lattice Fourier–Weyl transforms. The amplitudes of the particle’s jumps to neighbouring positions are controlled by a complex-valued dual root lattice hopping function with finite support. The solutions of the time-independent Schrödinger equation together with the eigenenergies of the quantum systems are explicitly determined. The matrix Hamiltonians and eigenenergies of the discrete models are exemplified for the rank two cases A 2 and C 2.

Curvature-induced noncommutativity of two different components of momentum for a particle on a hypersurface

As a nonrelativistic particle constrained to remain on an (N − 1)-dimensional ((N ≥ 2)) hypersurface embedded in an N-dimensional Euclidean space, two different components pi and p j (i, j = 1, 2, 3,… N) of the Cartesian momentum of the particle are not mutually commutative, and explicitly commutation relations depend on products of positions and momenta in uncontrollable ways. The generalized Dupin indicatrix of the hypersurface, a local analysis technique, is utilized to explore the dependence of the noncommutativity on the curvatures around a local point of the hypersurface. The first finding is that the noncommutativity can be grouped into two categories; one is the product of a sectional curvature and the angular momentum, and another is the product of a principal curvature and the momentum. The second finding is that, for a small circle lying a tangential plane covering the local point, the noncommutativity leads to a rotation operator and the amount of the rotation is an angle anholonomy; and along each of the normal sectional curves centering the given point the noncommutativity leads to a translation plus an additional rotation and the amount of the rotation is one half of the tangential angle change of the arc.

Probability flow for a free particle: new quantum effects

New quantum probability flow bounds and associated eigenfunctions are determined numerically for a free non-relativistic particle, with momentum lying in the range (p 0, ∞), for each fixed p 0 chosen in the range (−∞ , ∞). It is found that as p 0 increases through positive values, the maximum possible probability backflow from right-to left (R to L), opposite to the direction of all contributing momenta, decreases monotonically from the well-known value ≈0.038452 at p 0 = 0 but never reaches 0. As p 0 decreases through negative values, the maximum R to L flow increases monotonically but never reaches 1. These new quantum effects are compared and contrasted with the corresponding classical behaviour. A surprising new effect is revealed: Even when p 0 is negative, L to R directed momenta contribute to the maximum R to L flow. The size of this contribution is indicated by comparing with the maximum R to L flow possible when only negative momenta with values between p 0 and 0 are allowed. The extended modeling admits a simple interpretation of the classical limit without the introduction of a mechanism external to the system, as an effective value of Planck’s constant approaches zero.

Analysis of nonrelativistic particles in noncommutative phase-space under new scalar and vector interaction terms

The Schrödinger equation in noncommutative phase space is considered with a combination of linear, quadratic, Coulomb and inverse square terms. Using the quasi exact ansatz approach, we obtain the energy eigenvalues and the corresponding wave functions. In addition, we discuss the results for various values of in noncommutative phase space and discuss the results via various figures.

Constraining the shear acceleration model for the X-ray emission of large-scale extragalactic jets

ABSTRACTThe nature of the intense X-ray emission from powerful extragalactic jets at large (>1 kpc) scale is still debated. The scenario that invokes the inverse Compton scattering of the cosmic microwave background by electrons is challenged by the lack of gamma-ray emission in the GeV band. An alternative assumes synchrotron emission by a distinct population of ultra-high energy electrons. Here, we present a concrete attempt to apply this scenario, exploring the specific model in which the ultra-high energy electrons are accelerated in a shear layer surrounding the jet. We limit the study to non-relativistic flows and particle acceleration is treated by a Fokker–Planck equation. The observed relation between low energy (radio, optical) and X-ray emission prompts us to assume that the required population of pre-accelerated particles is provided by a shock responsible for the acceleration of the electrons emitting at low frequencies. We apply the model to the emission of the principal knots of the jets of PKS 0637–752 and PKS 1136–135, two of the best-studied objects. For the set of fiducial parameters adopted, the condition that the jet power does not exceeds a limiting value of 1048 erg s−1 constrains the magnetic field above $10\, \mu$G and indicates moderate beaming (δ ≃ 2) for PKS 0637–752. For both sources, the requirement that acceleration of the electrons proceeds faster than radiative cooling can be met if the magnetic turbulence in the shear layer follows a Kolmogorov spectrum, I(k) ∝ k−q with q = 5/3, but cannot satisfied in the Bohm-like case (q = 1).

Geometric scattering in the presence of line defects

A non-relativistic scalar particle moving on a curved surface undergoes a geometric scattering whose behavior is sensitive to the theoretically ambiguous values of the intrinsic and extrinsic curvature coefficients entering the expression for the quantum Hamiltonian operator. This suggests using the scattering data to settle the ambiguity in the definition of the Hamiltonian. It has recently been shown that the inclusion of point defects on the surface enhances the geometric scattering effects. We perform a detailed study of the geometric scattering phenomenon in the presence of line defects for the case that the particle is confined to move on a Gaussian bump and the defect(s) are modeled by delta-function potentials supported on a line or a set of parallel lines normal to the scattering axis. In contrast to a surface having point defects, the scattering phenomenon associated with this system is generically geometric in nature in the sense that for a flat surface the scattering amplitude vanishes for all scattering angles $\theta$ except $\theta=\theta_0$ and $\pi-\theta_0$, where $\theta_0$ is the angle of incidence. We show that the presence of the line defects amplifies the geometric scattering due to the Gaussian bump. This amplification effect is particularly strong when the center of the bump is placed between two line defects.

Possible Explanation of the Dynamics of the Universe Expansion without Dark Energy and without New Gravitational Degrees of Freedom

The commonly accepted view is that the Universe is currently in the dark energy dominance era (estimated to start about 5 billion years ago)—the era where yet unknown dark energy dominates over the gravitation and is responsible for the observed acceleration of the Universe expansion. In the present paper, we consider a “gas” of a large number of gravitating neutral nonrelativistic particles having a practically infinite lifetime and zero or very little interaction with the rest of the matter (neutrinos could be an example). One of the central points is the application of Dirac’s Generalized Hamiltonian Dynamics to pairs of these particles. Another central point is the application of the virial theorem to pairs of zero total energy. We demonstrate that as a result, the gravitational interaction within the entire system effectively decreases. Together with the observational fact of the Universe rotation (according to Shamir’s study of 2020), this model provides a possible explanation of the entire history of the Universe expansion: both the era of the decelerating expansion and the current era of the accelerated expansion.

Features of Nondissipative Channeling of Moving Particles Near a Conductor with Current

The specific features of free (outside a conductor) motion of charged particles in the field of a vector potential produced by a direct current flowing in a cylindrical or a flat conductor are considered. It is shown that when particles with negative charge move along the current direction (as well as when positively charged particles move in the opposite direction), the process of interaction of charges with the vector potential of the current corresponds to the presence of a very deep potential well whose minimum lies outside the conductor. This position of the minimum of the potential well corresponds to the flow of a current whose strength does not exceed several kiloamperes for electrons and positrons and several tens of kiloamperes for protons. When these values are exceeded, the minimum shifts into the bulk of the conductor. When the current decreases or the longitudinal energy of a particle increases, the position of the minimum varies in the range from near the surface of the conductor to values that are many tens of times greater than the thickness (diameter) of the conductor. The depth of the potential well increases with increasing energy of a particle and may reach tens and hundreds of kiloelectronvolts even for nonrelativistic particles. The structure of the potential well near the surface of a flat conductor with current corresponds to a harmonic oscillator whose frequency depends on the current strength, the thickness of the flat conductor, and the particle energy. The presence of such features makes it possible to implement a nondissipative channeling regime outside the conductor and the transportation of particles over a long distance.

Quantum-Mechanical Brayton Engine for the Nonrelativistic Particle Trapped in a Symmetric Potential Box

A theoretical quantum Brayton engine research has been carried out using a potential box system to increase its thermal efficiency. The method applied in this research is a classical thermodynamics system model in the form of a piston tube containing a monatomic ideal gas analogous to a quantum model in the form of a potential box containing one particle. The efficiency formulation of the quantum Brayton engine obtained from this study is following the classical version. However, the efficiency value obtained on a quantum Brayton engine is higher when compared to its classic. It happens because the value of the Laplace constant owned by the Brayton quantum version is 3, while the classic version is 5/3.

Electric quadrupole moment of a neutral non-relativistic particle in the presence of screw dislocation

In this contribution, we investigate the interaction between electric and magnetic fields with an electric quadrupole moment of a spinless particle moving in an elastic medium which has a topological defect (screw dislocation). By considering this interaction, the Schrödinger equation is exactly solved by using the analytical method. Thus, the eigenfunction and energy eigenvalues for two configurations are found. Meanwhile, by observing a shift in the angular momentum quantum number, the energy eigenvalues and the wave function of the system are modified, due to the screw dislocation in the medium.

Energy injection in pre-recombination era and EDGES detection

We study the possibility of explaining the recent EDGES detection by an energy injection in the pre-recombination era. Our aim is to show that the residue of this energy injection could give the resultant increase in the energy density at frequencies xe ≡ hν/(kT) ≃ 10−3, which is needed to explain the EDGES result. We consider two models of energy injection: Gaussian profile with a fixed redshift of injection and radiative decay of a non-relativistic particle. We show that the energy injection should occur in the redshift range z≲ 4 × 103 to prevent free-free processes from thermalizing the injected energy. The injected energy should be nearly 200–1000 times the CMB intensity at xe ≃ 10−3 to obtain the requisite residue. A large fraction of the injected energy gets thermalized and therefore distorts the CMB spectrum. We compute CMB spectral distortion for both the models and show that the fractional change in CMB energy density, Δ ρ CMB/ρ CMB ≃ 10−6, which might be detectable with the proposed experiment PIXIE . We also outline the implication of our proposed scenario for CMB anisotropies.

Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in the background of screw dislocations with a rotating frame

In this study, we considered a moving particle with a magnetic quadrupole moment in an elastic medium in the presence of a screw dislocation. We assumed a radial electric field in a rotating frame that leads a uniform effective magnetic field perpendicular to the plane of motion. We solved the Schrödinger equation to derive wave and energy eigenvalue functions by employing analytical methods for two interaction configurations: in the absence of potential and in the presence of a static scalar potential. Due to the topological defect in the medium, we observed a shift in the angular momentum quantum number which affects the energy eigenvalues and the wave function of the system.

Canonical formulation for a non-relativistic spinning particle coupled to gravity

We systematically derive an action for a nonrelativistic spinning particle in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the corresponding action in a curved background. It is achieved by following our recently developed technique of localising the flat space Galilean symmetry (Banerjee et al 2014 Phys. Lett. B 737 369; Banerjee et al 2015 Phys. Rev. D 91 084021; Banerjee et al 2015 Class. Quantum Grav. 32 045010). The coupling of the spinning particle to a Newton–Cartan background is obtained naturally. The equation of motion is found to differ from the geodesic equation, in agreement with earlier findings. Results for both the flat space limit and the spinless theory (in curved background) are reproduced. Specifically, the geodesic equation is also obtained in the latter case.