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Sudhir R. Jain

Publications and source records attributed to Sudhir R. Jain.

At least 19 recordsLinked to original sources

Crossover between the zeptosecond and attosecond physics

Nuclear orbiting resonances have been revealed at the sub-barrier energies as an atomic phenomenon by means of x-ray spectroscopy experiments. This interpretation is supported by several phenomenological models and theoretical estimates of the nuclear orbiting timescale and cross-section, inelastic scattering cross section including both nuclear and Coulomb excitation, and the Wigner-Smith time delay. We demonstrate that a multi-photon exchange during nuclear orbiting is responsible for an atomic excitation. Furthermore, proximity of the projectile and target nucleus during the nuclear orbiting modifies the effective charge of the projectile. Even though this orbiting induced excitation is triggered in zeptoseconds, it can still be observed in the attosecond time scale because of the Wigner-Smith time delay inherent to autoionization. Thus, we demonstrate the crossover between the zeptosecond and attosecond time scales which are native to nuclear and atomic physics, respectively. Markedly, this crossover may be the reason for x-ray production from ultra short nuclear processes ($\leq 10^{-21}$ sec). This explanation is likely to resolve the fission time scale anomaly and can stimulate cross-disciplinary research ranging from solid state to high-energy physics.

physics.atom-ph↗

Quasi-integrability and nonlinear resonances in cold atoms under modulation

Quantum dynamics of a collection of atoms subjected to phase modulation has been carefully revisited. We present an exact analysis of the evolution of a two-level system (represented by a spinor) under the action of a time-dependent matrix Hamiltonian. The dynamics is shown to evolve on two coupled potential energy surfaces, one of them binding while the other one scattering type. The dynamics is shown to be quasi-integrable with nonlinear resonances. The bounded dynamics with intermittent scattering at random moments presents the scenario reminiscent to Anderson and dynamical localization. We believe that a careful analytical investigation of a multi-component system which is classically non-integrable is relevant to many other fields, including quantum computation with multi-qubit system.

quant-ph↗

Protection of qubits by nonlinear resonances

We show that quantized superconducting circuits are non-integrable at the classical level of description, adorned by nonlinear resonances amidst stochastic sea. The spectral fluctuations of these quasi-integrable systems exhibit intermediate behaviour between regularity and chaos. The distribution function of ratios of adjacent spacings, and, nearest-neighbour spacing distribution functions attest to the occurrence of "mild chaos". Based on these features, we propose criteria for protection of qubits from decoherence which amounts to choosing the parameters of the system in a way that the system resides as close as possible to the elliptic point of the primary nonlinear resonance of the corresponding classical system.

quant-ph↗

Neutrino spin-flavor oscillations in solar environment

We study the phenomenon of neutrino spin-flavor oscillations due to solar magnetic fields. This allows us to examine how significantly the electron neutrinos produced in the solar interior undergo a resonant spin-flavor conversion. We construct analytical models for the solar magnetic field in all the three regions of the Sun. Neutrino spin-flavor oscillations in these magnetic fields are examined by studying the level crossing phenomenon and comparing the two cases of zero and non-zero vacuum mixing respectively. Results from the Borexino experiment are used to place an upper limit on the magnetic field in the solar core. Related phenomena such as effects of matter on neutrino spin transitions and differences between Dirac and Majorana transitions in the solar magnetic fields are also discussed.

hep-ph↗

Localization in one-dimensional relativistic quantum mechanics

We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-$\frac{1}{2}$ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the case of a large number of identical barriers spread randomly in one dimension. The particular case when the incident particle has three component momentum and shows spin-flip phenomena is also considered. Our calculations suggest that the incident relativistic particle shows localization behaviour similar to that of Anderson localization. A number of results which are generalizations of the non-relativistic case are also obtained.

cond-mat.dis-nn↗

Non-adiabatic transitions and non-equilibrium statistics of deforming nuclei

We establish a connection between macroscopic "heating or cooling" of a finite many-body quantum system and the non-adiabatic Landau-Zener-Stückelberg transitions between its quantum states. We have considered the well-known Nilsson model for describing the single-particle states of nuclei and subject the system to a random walk in the deformation space. This subsumes modelling of an evolving many-body system where the dynamics is chaotic. We discover a universality in the distribution of final "temperatures", beginning with a canonical equilibrium at some temperature $T$. The quantum system is thrown out of equilibrium where free energy and work undergo fluctuations. These fluctuations are shown to respect Jarzynski inequality, and, the Bochkov-Kuzovlev equalities. We believe that this study will pave the way towards understanding non-equlibrium phenomena in other finite quantum systems like metallic clusters, quantum dots, and others.

nucl-th↗

Ignatyuk damping factor: A semiclassical formula

Data on nuclear level densities extracted from transmission data or gamma energy spectrum store the basic statistical information about nuclei at various temperatures. Generally this extracted data goes through model fitting using computer codes like CASCADE. However, recently established semiclassical methods involving no adjustable parameters to determine the level density parameter for magic and semi-magic nuclei give a good agreement with the experimental values. One of the popular ways to paramaterize the level density parameter which includes the shell effects and its damping was given by Ignatyuk. This damping factor is usually fitted from the experimental data on nuclear level density and it comes around 0.05 $MeV^{-1}$. In this work we calculate the Ignatyuk damping factor for various nuclei using semiclassical methods.

nucl-th↗

Entropy of hard square lattice gas with $k$ distinct species of particles: coloring problems and vertex models

Coloring the faces of 2-dimensional square lattice with $k$ distinct colors such that no two adjacent faces have the same color is considered by establishing connection between the $k$ coloring problem and a generalized vertex model. Associating the colors with $k$ distinct species of particles with infinite repulsive force between nearest neighbors of the same type and zero chemical potential $μ$ associated with each species, the number of ways $[W(k)]^N$ for large $N$ is related to the entropy of the {\it{hard square lattice gas}} at close packing of the lattice, where $N$ is the number of lattice sites. We discuss the evaluation of $W(k)$ using transfer matrix method with non-periodic boundary conditions imposed on at least one dimension and show the characteristic Toeplitz block structure of the transfer matrix. Using this result, we present some analytical calculations for non-periodic models that remain finite in one dimension. The case $k=3$ is found to approach the exact result obtained by Lieb for the residual entropy of ice with periodic boundary conditions. Finally, we show, by explicit calculation of the contribution of subgraphs and the series expansion of $W(k)$, that the genenralized Pauling type estimate(which is based on mean field approximation) dominates at large values of $k$. We thus also provide an alternative series expansion for the chromatic polynomial of a regular square graph.

math-ph↗

Exact eigenfunction amplitude distributions of integrable quantum billiards

The exact probability distributions of the amplitudes of eigenfunctions, $Ψ(x, y)$, of several integrable planar billiards are analytically calculated and shown to possess singularities at $Ψ= 0$; the nature of this singularity is shape-dependent. In particular, we prove that the distribution function for a rectangular quantum billiard is proportional to the complete elliptic integral, ${\bf K}(1 - Ψ^2)$, and demonstrate its universality, modulo a weak dependence on quantum numbers. On the other hand, we study the low-lying states of nonseparable, integrable triangular billiards and find the distributions thereof to be described by the Meijer G-function or certain hypergeometric functions. Our analysis captures a marked departure from the Gaussian distributions for chaotic billiards in its survey of the fluctuations of the eigenfunctions about $Ψ= 0$.

math-ph↗

Noncyclic geometric phases and helicity transitions for neutrino oscillations in a magnetic field

We show that neutrino spin and spin-flavor transitions involve nonvanishing geometric phases. The geometric character of neutrino spin rotation is explored by studying the neutrino spin trajectory in the projective Hilbert space representation and its relation to the geometric phase. Analytical expressions are derived for noncyclic geometric phases. Several calculations are performed for different cases of rotating and nonrotating magnetic fields in the context of solar neutrinos and neutrinos produced inside neutron stars. Also the effects of adiabaticity, critical magnetic fields and cross boundary effects in the case of neutrinos emanating out of neutron stars are examined.

hep-ph↗

Nodal portraits of quantum billiards: Domains, lines, and statistics

We present a comprehensive review of the nodal domains and lines of quantum billiards, emphasizing a quantitative comparison of theoretical findings to experiments. The nodal statistics are shown to distinguish not only between regular and chaotic classical dynamics but also between different geometric shapes of the billiard system itself. We discuss, in particular, how a random superposition of plane waves can model chaotic eigenfunctions and highlight the connections of the complex morphology of the nodal lines thereof to percolation theory and Schramm-Loewner evolution. Various approaches to counting the nodal domains---using trace formulae, graph theory, and difference equations---are also illustrated with examples. The nodal patterns addressed pertain to waves on vibrating plates and membranes, acoustic and electromagnetic modes, wavefunctions of a "particle in a box'" as well as to percolating clusters, and domains in ferromagnets, thus underlining the diversity---and far-reaching implications---of the problem.

quant-ph↗

Semiclassical triton

The symmetric components of the spatial part of $S$- and $D$- states' wavefunctions for triton $(^{3}H)$ are investigated utilizing semiclassical expansion (in the powers of $\hbar$). Analysis of the diagonalized Hamiltonian reveals the existence of two different mass states within the ground state of triton. We have solved the coupled differential equations for the two admixed states $^{2}S_{1/2}$ and $^{4}D_{1/2}$ owing to tensor interactions exploiting classical WKB-theory using phenomenological Feshbach-Pease potentials. The relative probability of the $D$-state is found to be in good agreement with the experimentally inferred value (4 - 5 \%).

nucl-th↗

Raising and lowering operators for quantum billiards

For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m, n$, the index which represents a class is $c = m\, \mbox{mod}\, k\,n$ for a natural number, $k$. We show here that the entire tower of states can be generated from an initially given state by application of the operators introduced here. Thus, these operators play the same role for billiards as raising and lowering operators in angular momentum algebra.

quant-ph↗

Truncated Calogero-Sutherland Models on a Circle

We investigate a quantum many-body system with particles moving on a circle and subject to two-body and three-body potentials. In this new class of models, that extrapolates from the celebrated Calogero-Sutherland model and a system with interactions among nearest and next-to-nearest neighbors, the interactions can be tuned as a function of range. We determine the exact ground state energy and wavefunction and obtain a part of the excitation spectrum.

quant-ph↗

A difference-equation formalism for the nodal domains of separable billiards

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in [Ann. Phys. 351, 1-12 (2014)]. The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

quant-ph↗

Geometric phase for neutrino propagation in magnetic field

The geometric phase for neutrinos propagating in an adiabatically varying magnetic field in matter is calculated. It is shown that for neutrino propagation in sufficiently large magnetic field the neutrino eigenstates develop a significant geometric phase. The geometric phase varies from 2$π$ for magnetic fields $\sim$ fraction of a micro gauss to $π$ for fields $\sim 10^7$ gauss or more. The variation of geometric phase with magnetic field parameters is shown and its phenomenological implications are discussed.

hep-ph↗

A finite-time exponent for random Ehrenfest gas

We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit.

nlin.CD↗

A nodal domain theorem for integrable billiards in two dimensions

Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, $ν$, of the eigenfunctions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, $ν$ satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of $m\mod kn$, given a particular $k$, for a set of quantum numbers, $m, n$. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations.

nlin.SI↗