arXiv subjects

V. Balakrishnan

Publications and source records attributed to V. Balakrishnan.

54 records · Page 3Linked to original sources

arXiv2016

Signatures of nonclassical effects in optical tomograms

Several nonclassical effects displayed by wave packets subject to generic nonlinear Hamiltonians can be identified and assessed directly from tomograms without attempting to reconstruct the Wigner function or the density matrix explicitly. We have demonstrated this for both single-mode and bipartite systems. We have shown that a wide spectrum of effects such as the revival phenomena, quadrature squeezing and Hong-Mandel and Hillery type higher-order squeezing in both the single-mode system and the double-well Bose-Einstein condensate can be obtained from appropriate tomograms in a straightforward manner. We have investigated entropic squeezing of the subsystem state of a bipartite system as it evolves in time, solely from tomograms. Further we have identified a quantifier of the extent of entanglement between subsystems which can be readily obtained from the tomogram and which mirrors the qualitative behavior of other measures of entanglement such as the subsystem von Neumann entropy and the subsystem linear entropy. The procedures that we have demonstrated can be readily adapted to multimode systems.

quant-ph↗

arXiv2015

Entanglement dynamics in a model tripartite quantum system

A system comprising a $Λ$-type or V-type atom interacting with two radiation fields exhibits, during its dynamical evolution, interesting optical phenomena such as electromagnetically-induced transparency (EIT) and a variety of nonclassical effects. Signatures of the latter are seen in the entanglement dynamics of the atomic subsystem and in appropriate field observables. Some of these effects have been experimentally detected, and have even been used to change the nonlinear optical properties of certain atomic media. It is therefore useful to investigate the roles played by specific initial states of the radiation fields, detuning parameters, field nonlinearities and the nature of field-atom couplings on EIT and on the entanglement between subsystems. We investigate these aspects in the framework of a simple model that captures the salient features of such tripartite entangled systems. Entanglement dynamics is shown to be very sensitive to the intensity-dependent atom-field couplings. Unexpected interesting features pertaining to the collapses and revivals of the atomic subsystem von Neumann entropy appear. These features could, in principle, be useful in enabling entanglement.

quant-ph↗

arXiv2014

Dynamics of an open quantum system interacting with a quantum environment

We examine the dynamics of subsystems of bipartite and tripartite quantum systems with nonlinear Hamiltonians. We consider two models which capture the generic features of open quantum systems: a three-level atom interacting with a single-mode radiation field, and a three-level atom interacting with two field modes which do not directly interact with each other. The entanglement of specific initially unentangled states of the atom-field system is examined through the time-varying subsystem von Neumann entropy (SVNE). The counterparts of near-revivals and fractional revivals of the initial state are clearly identifiable in the SVNE in all cases where revival phenomena occur. The Mandel $Q$ parameter corresponding to the photon number of a radiation field is obtained as a function of time in both models. In those cases where revivals are absent, a time series analysis of the mean photon number reveals a variety of ergodicity properties (as manifested in return maps, recurrence-time distributions and Lyapunov exponents), depending on the strength of the nonlinearity and the degree of coherence of the initial state of the radiation field(s).

quant-ph↗

arXiv2010

Effective Bandwidth Utilization in IEEE802.11 for VOIP

Voice over Internet protocol (VoIP) is one of the most important applications for the IEEE 802.11 wireless local area networks (WLANs). For network planners who are deploying VoIP over WLANs, one of the important issues is the VoIP capacity. VoIP bandwidth consumption over a WAN is one of the most important factors to consider when building a VoIP infrastructure. Failure to account for VoIP bandwidth requirements will severely limit the reliability of a VoIP system and place a huge burden on the WAN infrastructure. Less bandwidth utilization is the key reasons for reduced number of channel accesses in VOIP. But in the QoS point of view the free bandwidth of atleast 1-5% will improve the voice quality. This proposal utilizes the maximum bandwidth by leaving 1-5% free bandwidth. A Bandwidth Data rate Moderation (BDM) algorithm has been proposed which correlates the data rate specified in IEEE802.11b with the free bandwidth. At each time BDM will calculate the bandwidth utilization before sending the packet to improve performance and voice quality of VoIP. The bandwidth calculation in BDM can be done by using Erlang and VOIP bandwidth calculator. Finally, ns2 experimental study shows the relationship between bandwidth utilization, free bandwidth and data rate. The paper concludes that marginal VoIP call rate has been increased by BDM algorithm.

cs.NI↗

arXiv2009

Recurrence properties of quantum observables in wave packet dynamics

We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time distributions, return maps and recurrence plots, we conclude that the dynamics of appropriate observables pertaining to the field can vary from quasiperiodicity to hyperbolicity, depending on the extent of the nonlinearity and of the departure from coherence of the initial state of the field. We establish that, in a simple bipartite model in which the field is effectively an open quantum system, a decaying exponential recurrence-time distribution, characteristic of a hyperbolic dynamical system, is associated with chaotic temporal evolution as characterized by a positive Liapunov exponent.

quant-ph↗

arXiv2007

Ergodicity properties of quantum expectation values in entangled states

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics of the total system is regular. The time series of the mean photon number is studied over a range of values of the ratio of the strength $γ$ of the nonlinearity to that of the inter-mode coupling $g$. We obtain the power spectrum, estimate the embedding dimension of the reconstructed phase space and the maximal Liapunov exponent $λ_{\rm max}$, and find the recurrence-time distribution of the coarse-grained dynamics. The dynamical behavior ranges from quasiperiodicity (for $γ/g \ll 1$) to chaos as characterized by $λ_{\rm max} > 0$ (for $γ/g \gtrsim 1$), and is interpreted.

quant-ph↗

arXiv2006

Wave packet dynamics of entangled two-mode states

We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in which the field mode is initially in a Fock state, a coherent state, or a photon-added coherent state. The counterparts of near-revivals and fractional revivals are shown to be clearly identifiable in the entropy of entanglement. The ``overlap fidelity'' of the system is another such indicator, and its behaviour corroborates that of the entropy of entanglement in the vicinity of near-revivals. The expectation values and higher moments of suitable quadrature variables are also examined, with reference to possible squeezing and higher-order squeezing.

quant-ph↗

arXiv2005

Non-classical properties of quantum wave packets propagating in a Kerr-like medium

We investigate non-classical effects such as fractional revivals, squeezing and higher-order squeezing of photon-added coherent states propagating through a Kerr-like medium.The Wigner functions corresponding to these states at the instants of fractional revivals are obtained, and the extent of non-classicality quantified.

quant-ph↗

arXiv2004

Analytic calculation of energy transfer and heat flux in a one-dimensional system

In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nature of the Fourier law for the model, and the nonlinear dependence of the rate of mechanical work on the stationary drift velocity of the tagged particle, are analyzed and elucidated.

cond-mat.stat-mech↗

arXiv2004

Wave packet dynamics of the matter wave field of a Bose-Einstein condensate

We show in the framework of a tractable model that revivals and fractional revivals of wave packets afford clear signatures of the extent of departure from coherence and from Poisson statistics of the matter wave field in a Bose-Einstein condensate, or of a suitably chosen initial state of the radiation field propagating in a Kerr-like medium.

quant-ph↗

arXiv2004

Signatures of wave packet revival phenomena in the expectation values of observables

Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially coherent wave packet in a Kerr-like medium), it is shown that distinctive signatures of these revivals and fractional revivals are displayed by the time evolution of the expectation values of physical observables and their powers, i.e., by experimentally measurable quantities. Moreover, different fractional revivals can be selectively identified by examining appropriate higher moments.

quant-ph↗

arXiv2001

Stochastically perturbed flows: Delayed and interrupted evolution

We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed evolution, in which the flow alternates with a quiescent state in which the variate remains frozen at its current value for random intervals of time; and interrupted evolution, in which the variate is also re-set in the quiescent state to a random value drawn from a fixed distribution. In the former case, the effect of the delay upon the first passage time statistics is analyzed. In the latter case, the conditions under which an extended stationary distribution can exist as a consequence of the competition between an attractor in the flow and the random re-setting are examined. We elucidate the role of the normalization condition in eliminating the singularities arising from the unstable critical points of the flow, and present a number of representative examples. A simple formula is obtained for the stationary distribution and interpreted physically. A similar interpretation is also given for the known formula for the stationary distribution in a full-fledged dichotomous flow.

cond-mat.stat-mech↗

arXiv2001

Velocity Correlations, Diffusion and Stochasticity in a One-Dimensional System

We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a non-vanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a $t^{-3}$ tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the position of any particle in the system reduces in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv1999

Quantum revivals, geometric phases and circle map recurrences

Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincaré recurrences for a rotation map: only three distinct revival times can occur, with specified weights. A link is thus established between quantum revivals and recurrences in a coarse-grained discrete-time dynamical system.

quant-ph↗

arXiv1999

Control of Wave Packet Revivals Using Geometric Phases

Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by varying the parameters in the Hamiltonian cyclically with a period T. Further, with the introduction of this natural time step T, the occurrence of near revivals can be mapped onto that of Poincaré recurrences in an irrational rotation map of the circle. The distinctive recurrence time statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.

quant-ph↗

arXiv1999

Ladder operators for isospectral oscillators

We present, for the isospectral family of oscillator Hamiltonians, a systematic procedure for constructing raising and lowering operators satisfying any prescribed `distorted' Heisenberg algebra (including the $q$-generalization). This is done by means of an operator transformation implemented by a shift operator. The latter is obtained by solving an appropriate partial isometry condition in the Hilbert space. Formal representations of the non-local operators concerned are given in terms of pseudo-differential operators. Using the new annihilation operators, new classes of coherent states are constructed for isospectral oscillator Hamiltonians. The corresponding Fock-Bargmann representations are also considered, with specific reference to the order of the entire function family in each case.

quant-ph↗

arXiv1999

Geometric phases for generalized squeezed coherent states

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The formalism is first applied to a general deformation of the oscillator involving both squeezing and displacement. Earlier results are shown to emerge as special cases. The analysis is then extended to multiphoton squeezed coherent states and the corresponding anholonomies deduced.

quant-ph↗

arXiv1999

Noise-amplitude dependence of the invariant density for noisy, fully chaotic one-dimensional maps

We present some analytic, non-perturbative results for the invariant density rho(x) for noisy one-dimensional maps at fully developed chaos. Under periodic boundary conditions, the Fourier expansion method is used to show precisely how noise makes rho(x) absolutely continuous and smoothens it out. Simple solvable models are used to illustrate the explicit dependence of rho(x) on the amplitude eta of the noise distribution, all the way from the case of zero noise (eta > 0) to the completely noise-dominated limit (eta=1).

chao-dyn↗