Dissipative Bose-Josephson junction coupled to bosonic baths

We investigate the effect of dissipation in a Bose-Josephson junction (BJJ) coupled to bath of bosons at two sites. Apart from the dynamical transition due to repulsive interactions, the BJJ undergoes a quantum phase transition by increasing the coupling strength with the bath modes. We analyze this system by mapping to an equivalent spin model coupled to the bosonic modes. The excitation energies and fluctuation of number imbalance are obtained within Holstein-Primakoff approximation, which exhibit vanishing of energy gap and enhanced quantum fluctuations at the critical coupling. We study the dynamics of BJJ using time dependent variational method and analyze stability of different types of steady states. As a special case we study in details the phase space dynamics of BJJ coupled to a single mode, which reveals diffusive and incoherent behaviour with increasing coupling to the bath mode. The dynamical steady states corresponding to the Pi-oscillation and self-trapped state become unstable in the region where their oscillation frequencies are in resonance with the bath modes. We investigate the time evolution of number imbalance and relative phase in presence of Ohmic bath with Gaussian noise to incorporate thermal fluctuations. Apart from damping of Josephson oscillations and transition to symmetry broken state for strong coupling we observe decay of Pi-oscillation and self-trapped state to the ground state as a result of dissipation. Variation of phase fluctuation with temperature of the bath shows similar behaviour as observed in experiment. Finally we discuss the experimental setup to study the observable effects of dissipation in BJJ

Stress controlled magnetic properties of Cobalt nanowires

We investigate the magnetic properties of a composite comprising of ferromagnetic Cobalt nanowires embedded in nanoporous anodized alumina template. We observe unusual increase in, the saturation magnetization and the coercive field, of the nanowires below 100 K. We also report the appearance of an unusual exchange bias effect in nanowires below 100 K. We argue our results can be understood on the basis of a competition between different magnetic energy scales induced by significant stresses acting on the nanowires at low temperatures. The composite behaves as an effective medium in which the magnetic anisotropy of nanowires can be conveniently controlled via stress on the nanowires.Comment: 16 pages, 7 figures, Submitte

Controlling spatiotemporal chaos and spiral turbulence in excitable media: A review

Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating spiral waves. Instabilities in these structures may lead to spatiotemporal chaos through spiral turbulence, which has been linked to clinically diagnosed conditions such as cardiac fibrillation. Usual methods for controlling such phenomena involve very large amplitude perturbations and have several drawbacks. There have been several recent attempts to develop low-amplitude control procedures for spatiotemporal chaos in excitable media which are reviewed in this paper. The control schemes have been broadly classified by us into three types: (i) global, (ii) non-global spatially-extended and (iii) local, depending on the way the control signal is applied, and we discuss the merits and drawbacks for each.Comment: 9 pages, 6 figures; A version of the work will appear as Chapter 32 in Handbook of Chaos Control, 2nd Revised edition, (Eds.) E Scholl and H G Schuster, Wiley-VCH, Berlin (2007

Phases and collective modes of hardcore Bose-Fermi mixture in an optical lattice

We obtain the phase diagram of a Bose-Fermi mixture of hardcore spinless Bosons and spin-polarized Fermions with nearest neighbor intra-species interaction and on-site inter-species repulsion in an optical lattice at half-filling using a slave-boson mean-field theory. We show that such a system can have four possible phases which are a) supersolid Bosons coexisting with Fermions in the Mott state, b) Mott state of Bosons coexisting with Fermions in a metallic or charge-density wave state, c) a metallic Fermionic state coexisting with superfluid phase of Bosons, and d) Mott insulating state of Fermions and Bosons. We chart out the phase diagram of the system and provide analytical expressions for the phase boundaries within mean-field theory. We demonstrate that the transition between these phases are generically first order with the exception of that between the supersolid and the Mott states which is a continuous quantum phase transition. We also obtain the low-energy collective excitations of the system in these phases. Finally, we study the particle-hole excitations in the Mott insulating phase and use it to determine the dynamical critical exponent $z$ for the supersolid-Mott insulator transition. We discuss experiments which can test our theory.Comment: 10 pages 6 Figs v2: Updated version with more refs and additional discussion

Emergence of two-phase behavior in markets through interaction and learning in agents with bounded rationality

Phenomena which involves collective choice of many agents who are interacting with each other and choosing one of several alternatives, based on the limited information available to them, frequently show switching between two distinct phases characterized by a bimodal and an unimodal distribution respectively. Examples include financial markets, movie popularity and electoral behavior. Here we present a model for this biphasic behavior and argue that it arises from interactions in a local neighborhood and adaptation & learning based on information about the effectiveness of past choices.Comment: 5 pages, 2 figures, to appear in "Practical Fruits of Econophysics", Proc. 3rd Nikkei Econophysics Symposium, Tokyo, Nov 2004 (Springer

A finite temperature study of ideal quantum gases in the presence of one dimensional quasi-periodic potential

We study the thermodynamics of ideal Bose gas as well as the transport properties of non interacting bosons and fermions in a one dimensional quasi-periodic potential, namely Aubry-Andr\'e (AA) model at finite temperature. For bosons in finite size systems, the effect of quasi-periodic potential on the crossover phenomena corresponding to Bose-Einstein condensation (BEC), superfluidity and localization phenomena at finite temperatures are investigated. From the ground state number fluctuation we calculate the crossover temperature of BEC which exhibits a non monotonic behavior with the strength of AA potential and vanishes at the self-dual critical point following power law. Appropriate rescaling of the crossover temperatures reveals universal behavior which is studied for different quasi-periodicity of the AA model. Finally, we study the temperature and flux dependence of the persistent current of fermions in presence of a quasi-periodic potential to identify the localization at the Fermi energy from the decay of the current.Comment: 25 pages, 12 figure

Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study

We study out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-Andr\'e (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the localized and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive induced delocalization even for systems which do not have a well defined semiclassical (and/or large N) limit. We demonstrate the presence of such signature by analyzing two different drive protocols for hardcore bosons chains leading to distinct physical phenomena and discuss experiments which can test our theory

Quantum Signature of Chaos and Thermalization in Kicked Dicke Model

We study the quantum dynamics of the kicked Dicke model(KDM) in terms of the Floquet operator and analyze the connection between the chaos and thermalization in this context. The Hamiltonian map is constructed by taking the classical limit of the Heisenberg equation of motion suitably to study the corresponding phase space dynamics which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed point analysis and calculation of the Lyapunov exponent(LE) provides us a complete picture of the onset of chaos in phase space dynamics. We carry out the spectral analysis of the Floquet operator which include the calculation of quasienergy spacing distribution, structural entropy and show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector and discuss how such periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics. We introduce the notion of an effective temperature and show that a microcanonical picture is emerging out in the thermodynamic limit indicating the thermalization occurring in such system.Comment: 10 pages, 10 figure

Drive Induced Delocalization in Aubry-Andr\'e Model

Motivated by the recent experiment by Bordia et al [Nat. Phys. 13, 460 (2017)], we study single particle delocalization phenomena of Aubry-Andr\'e (AA) model subjected to periodic drives. In two distinct cases we construct an equivalent classical description to illustrate that the drive induced delocalization phenomena stems from an instability and onset of chaos in the underlying dynamics. In the first case we analyze the delocalization and the thermalization in a time modulated AA potential with respect to driving frequency and demonstrate that there exists a threshold value of the amplitude of the drive. In the next example, we show that the periodic modulation of the hopping amplitude leads to an unusual effect on delocalization with a non-monotonic dependence on the driving frequency. Within a window of such driving frequency a delocalized Floquet band with mobility edge appears, exhibiting multifractality in the spectrum as well as in the Floquet eigenfunctions. Finally, we explore the effect of interaction and discuss how the results of the present analysis can be tested experimentally

Phases, collective modes, and non-equilibrium dynamics of dissipative Rydberg atoms

We use a density matrix formalism to study the equilibrium phases and non-equilibrium dynamics of a system of dissipative Rydberg atoms in an optical lattice within mean-field theory. We provide equations for the fixed points of the density matrix evolution for atoms with infinite on-site repulsion and analyze these equations to obtain their Mott insulator- superfluid (MI-SF) phase boundary. A stability analysis around these fixed points provides us with the excitation spectrum of the atoms both in the MI and SF phases. We study the nature of the MI-SF critical point in the presence of finite dissipation of Rydberg excitations, discuss the fate of the superfluidity of the atoms in the presence of such dissipation in the weak-coupling limit using a coherent state representation of the density matrix, and extend our analysis to Rydberg atoms with finite on-site interaction via numerical solution of the density matrix equations. Finally, we vary the boson (atom) hopping parameter $J$ and the dissipation parameter $\Gamma$ according to a linear ramp protocol. We study the evolution of entropy of the system following such a ramp and show that the deviation of the entropy from its steady state value for the latter protocol exhibits power-law behavior as a function of the ramp time. We discuss experiments which can test our theory.Comment: v2 10 pages 8 figs; minor typos correcte