Time-dependent Effective Mass Research Articles

Dynamics of the free time-dependent effective mass

The consensus is that an object with a large mass will not manifest quantum behavior. Therefore, we expect that the quantumness of a time-dependent effective mass (TDEM) will erase after a long time when the mass profile continuously grows with time. However, the present article depicts that the Wigner quasi-probability distribution (WQD) will manifest an entanglement behavour forever for two spatially separated free TDEM. The time-dependent Schr\"{o}dinger equation for a free particle with TDEM is solved with the help of Lewis-Riesenfeld phase space invariant method. WQD for the system of two identical TDEM with quadratically increasing mass profile shows that the particles are never separated. In particular, their reminiscent is present at the origin of the phase-space forever.

Eliminating the LIGO bounds on primordial black hole dark matter

Primordial black holes (PBHs) in the mass range (30–100) M⊙ are interesting candidates for dark matter but are tightly constrained by the LIGO merger rate. In deriving these constraints, PBHs were treated as constant Schwarzschild masses. A careful analysis of cosmological black holes however leads to a time-dependent effective mass. This implies stricter conditions for binary formation, so that the binaries formed merge well before LIGO's observations. The observed binaries are those coalescing within galactic halos, at a rate consistent with LIGO data. This reopens the possibility of LIGO mass PBH dark matter.

Schwinger mechanism during inflation

We revisit the efficiency of Schwinger mechanism in creating charged pairs during inflation. We consider a minimal setup of inflation in which the inflaton field is a complex scalar field charged under a $U(1)$ gauge field. There is a time dependent conformal coupling which pumps energy from the inflaton field to the gauge field to furnish a nearly constant background electric field energy density to drive the Schwinger mechanism. The coupling between the gauge field and the scalar field induces a time dependent effective mass for the inflaton field. The requirement of a long period of slow-roll inflation causes the Schwinger mechanism to be highly inefficient during inflation. The non-perturbative Schwinger mechanism can be relevant only towards the end of inflation and only on very small scales. This is in contrast to hypothetical models studied in literature in which the complex scalar field is a test field and a constant electric field is imposed on the dS background by hand. We calculate the number of pairs of charged particles created perturbatively during inflation. We show that it is proportional to the amplitude of the quadrupolar statistical anisotropy and it is very small. Consequently, the back-reactions of created particles on magnetogenesis on large scales are negligible.

Wave packet dynamics for a system with position and time-dependent effective mass in an infinite square well

The problem of a particle with position and time-dependent effective mass in a one-dimensional infinite square well is treated by means of a quantum canonical formalism. The dynamics of a launched wave packet of the system reveals a peculiar revival pattern that is discussed.

The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass**Supported by the National Natural Science Foundation of China under Grant No 11275100, and the K.C. Wong Magna Foundation of Ningbo University.

We investigate the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the harmonic potential theorem wave function when both the effective mass and frequency are static. An example of application is also given.

SELF-ACCELERATING UNIVERSE IN NONLINEAR MASSIVE GRAVITY

We discuss the self-accelerating universe solutions in the framework of the potentially ghost-free, nonlinear massive gravity theory recently proposed by de Rham–Gabadadze–Tolley. The theory allows general Friedmann–Robertson–Walker solutions with negative curvature. The contribution of the mass terms at the background level is an effective cosmological constant term depending on the parameters of the theory. We also discuss the cosmological perturbations in these backgrounds, as well as similar solutions of the extended versions of the theory; the actions of the scalar and vector degrees do not undergo a modification with respect to general relativity, while the two polarizations of gravity waves acquire a time-dependent effective mass term. This may lead to a modification of the stochastic gravitational wave spectrum.

Cosmological perturbations of self-accelerating universe innonlinear massive gravity

We study cosmological perturbations of self-accelerating universe solutions in the recently proposed nonlinear theory of massive gravity, with general matter content. While the broken diffeomorphism invariance implies that there generically are 2 tensor, 2 vector and 2 scalar degrees of freedom in the gravity sector, we find that the scalar and vector degrees have vanishing kinetic terms and nonzero mass terms. Depending on their nonlinear behavior, this indicates either nondynamical nature of these degrees or strong couplings. Assuming the former, we integrate out the 2 vector and 2 scalar degrees of freedom. We then find that in the scalar and vector sectors, gauge-invariant variables constructed from metric and matter perturbations have exactly the same quadratic action as in general relativity. The difference from general relativity arises only in the tensor sector, where the graviton mass modifies the dispersion relation of gravitational waves, with a time-dependent effective mass. This may lead to modification of stochastic gravitational wave spectrum.

Semiclassical wave packet dynamics in Schrödinger equations with periodic potentials

We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated (both, in space and in frequency) around the effective semiclassical phase-space flow obtained by Peierl's substitution, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schrodinger equation with time-dependent effective mass. The corresponding adiabatic decoupling of the slow and fast degrees of freedom is shown to be valid up to Ehrenfest time scales.

Kinetic theory for non-Hermitian dynamics of waves in shear flow

Fluctuations in an ambient shear flow obey “non-Hermitian” evolution equations, and hence, the conventional kinetic equation for waves does not apply. Introducing a time-dependent effective mass (modeling the phase-mixing effect) and a potential term (including the stretching effect), we may cast the wave equation in a Hamiltonian form, which allows us to formulate a kinetic equation that can capture the nonconservative nature of a shear-flow system.

Exact quantum theory of noninteracting electrons with time-dependent effectivemass in a time-dependent magnetic field

We investigated the quantum states of a free electron with time-dependenteffective mass subjected to a time-dependent magnetic field by solving theSchrödinger equation under the choice of Landau and symmetric gauges. Usingthe invariant operator and unitary transformation methods together, wederived exact wavefunctions of the system. The wavefunctions rely on thesolution of associated classical dynamical systems. We confirmed that thequantum analysis of the system under the two gauges coincides mutually.

Correlated charged pions from chiral dynamics in high-energy nuclear collisions

It is expected that chiral symmetry is approximately restored in the very excited matter produced in a high-energy nuclear collision and that the chiral order parameter will thereafter quickly relax towards its aligned vacuum value. This non-equilibrium evolution of the environment endows the pionic degrees of freedom with a time-dependent effective mass and this agency, in turn, may create correlated soft pions that could provide specific observable signatures of the chiral dynamics that are based solely on charged pions.

Probing chiral dynamics by charged-pion correlations

The environment generated in the midrapidity region of a high-energy nuclear collision endows the pionic degrees of freedom with a time-dependent effective mass. Its specific evolution provides a mechanism for the production of back-to-back charge-conjugate pairs of soft pions which may present an observable signal of the nonequilibrium dynamics of the chiral order parameter.

Unraveling critical dynamics: The formation and evolution of textures

We study the formation of topological textures in a nonequilibrium phase transition of an overdamped classical O(3) model in 2+1 dimensions. The phase transition is triggered through an external, time-dependent effective mass, parameterized by quench timescale \tau. When measured near the end of the transition the texture separation and the texture width scale respectively as \tau^(0.39 \pm 0.02) and \tau^(0.46 \pm 0.04), significantly larger than \tau^(0.25) predicted from the Kibble-Zurek mechanism. We show that Kibble-Zurek scaling is recovered at very early times but that by the end of the transition the power-laws result instead from a competition between the length scale determined at freeze-out and the ordering dynamics of a textured system. In the context of phase ordering these results suggest that the multiple length scales characteristic of the late-time ordering of a textured system derive from the critical dynamics of a single nonequilibrium correlation length. In the context of defect formation these results imply that significant evolution of the defect network can occur before the end of the phase transition. Therefore a quantitative understanding of the defect network at the end of the phase transition generally requires an understanding of both critical dynamics and the interactions among topological defects.

Time-dependent tunneling of wave-packets through heterostructures in an applied field

We investigate time-dependent tunneling of wave-packets through heterostructures by numerically solving the time-dependent effective mass Schrödinger equation. In particular, we analyze the effect of the form of the initial wave-packet on the energy-dependent transmission coefficient, discuss various time-scales related to resonant tunneling, and study effects of applied fields.