[Show abstract][Hide abstract] ABSTRACT: We study domain kinetics in ferroelectric films, subsequent to a rapid quench below the critical temperature. We model the kinetics via the time-dependent Ginzburg-Landau (TDGL) equation for the Ginzburg-Landau-Devonshire (GLD) free energy, which is a functional of the electric polarization vector (P) over right arrow = (P-x, P-y). The nature of ordering dynamics depends on the strength of coupling (alpha) between P-x and P-y. For alpha = 1, domain growth is mediated by the annihilation of vortex defects with the growth law L(t) similar to (t/ln t)(1/2). For alpha not equal 1, the corresponding defects are sharp interfaces between four-fold-degenerate ground states. The resultant growth law is purely diffusive: L(t) similar to t(1/2). Copyright (C) EPLA, 2013
[Show abstract][Hide abstract] ABSTRACT: The coupling of a mesoscopic system with its environment usually causes total
decoherence: at long times the reduced density matrix of the system evolves in
time to a limit which is independent of its initial value, losing all the
quantum information stored in its initial state. Under special circumstances, a
subspace of the system's Hilbert space remains coherent, or "decoherence free",
and the reduced density matrix approaches a non-trivial limit which contains
information on its initial quantum state, despite the coupling to the
environment. This situation is called "partial decoherence". Here we find the
conditions for partial decoherence for a mesoscopic system (with $N$ quantum
states) which is coupled to an environment. When the Hamiltonian of the system
commutes with the total Hamiltonian, one has "adiabatic decoherence", which
yields N-1 time-independent combinations of the reduced density matrix
elements. In the presence of a magnetic flux, one can measure circulating
currents around loops in the system even at long times, and use them to
retrieve information on the initial state. For N=2, we demonstrate that partial
decoherence can happen only under adiabatic decoherence conditions. However,
for $N>2$ we find partial decoherence even when the Hamiltonian of the system
does not commute with the total Hamiltonian, and we obtain the general
conditions for such non-adiabatic partial decoherence. For an electron moving
on a ring, with $N>2$ single-level quantum dots, non-adiabatic partial
decoherence can arise only when the total flux through the ring vanishes (or
equals an integer number of flux quanta), and therefore there is no asymptotic
circulating current.
[Show abstract][Hide abstract] ABSTRACT: An effort based on the kinetic model allowed by Landau-Ginzburg-Devonshire
theory is presented here. The formation of vortex, antivortex states in
ferroelectric films are reported and theoretically explained. Phase transition
in toroidal moment is observed. Vortex-antivortex-vortex (V-AV-V) triplet is
generated by applying inhomogeneous transverse static localized fields in x-y
plane. A specific boundary condition is used to keep the spirit of vortex state
i.e. the net polarization across the boundary is always zero. %This is neither
a periodic nor an open circuit electric boundary condition.
[Show abstract][Hide abstract] ABSTRACT: We consider a prototypical system of an infinite range transverse field Ising
model coupled to a bosonic bath. By integrating out the bosonic degrees, an
effective anisotropic Heisenberg model is obtained for the spin system. The
phase diagram of the latter is calculated as a function of coupling to the heat
bath and the transverse magnetic field. Collective excitations at low
temeratures are assessed within a spin-wave like analysis that exhibits a
vanishing energy gap at the quantum critical point. We also consider another
limit where the system reduces to a generalized spin-boson model of two
interacting spins. By increasing the coupling strength with the heat bath, the
two-spin wavefunction changes from an entangled state to a factorized state of
two spins which are aligned along the transverse field. We also discuss the
possible realization and application of the model to different physical
systems.
[Show abstract][Hide abstract] ABSTRACT: The qubit (or a system of two quantum dots) has become a standard paradigm
for studying quantum information processes. Our focus is Decoherence due to
interaction of the qubit with its environment, leading to noise. We consider
quantum noise generated by a dissipative quantum bath. A detailed comparative
study with the results for a classical noise source such as generated by a
telegraph process, enables us to set limits on the applicability of this
process vis a vis its quantum counterpart, as well as lend handle on the
parameters that can be tuned for analyzing decoherence. Both Ohmic and
non-Ohmic dissipations are treated and appropriate limits are analyzed for
facilitating comparison with the telegraph process.
[Show abstract][Hide abstract] ABSTRACT: The time evolution of a qubit, consisting of two single-level quantum dots,
is studied in the presence of telegraph noise. The dots are connected by two
tunneling paths, with an Aharonov-Bohm flux enclosed between them. Under
special symmetry conditions, which can be achieved by tuning gate voltages,
there develops partial decoherence: at long times, the off-diagonal element of
the reduced density matrix (in the basis of the two dot states) approaches a
non-zero value, generating a circulating current around the loop. The flux
dependence of this current contains full information on the initial quantum
state of the qubit, even at infinite time. Small deviations from this symmetry
yield a very slow exponential decay towards the fully-decoherent limit.
However, the amplitudes of this decay also contain the full information on the
initial qubit state, measurable either via the current or via the occupations
of the qubit dots.
[Show abstract][Hide abstract] ABSTRACT: We employ the Ginzburg–Landau–Devonshire free energy theory to construct a set of time-dependent ordinary differential equations in order to model the interaction dynamics of the tip of an atomic force microscope (AFM) with the surface of a ferroelectric thin film. Using this method we obtain (i) domain profile and (ii) domain nucleation which starts under the AFM tip. Since ferroelectrics are piezoelectric, the electromechanical coupling considered in our equations causes polarization to oscillate with the same frequency with which the AFM tip vibrates.
[Show abstract][Hide abstract] ABSTRACT: Growing colonies of bacteria on the surface of thin agar plates exhibit fractal patterns as a result of nonlinear response to environmental conditions, such as nutrients, solidity of the agar medium and temperature. Here, we examine the effect of glucose on pattern formation by growing colonies of Bacillus thuringiensis isolate KPWP1. We also present the theoretical modeling of the colony growth of KPWP1 and the associated spatio-temporal patterns. Our experimental results are in excellent agreement with simulations based on a reaction-diffusion model that describes diffusion-limited aggregation and branching, in which individual cells move actively in the periphery, but become immotile in the inner regions of the growing colony. We obtain the Hausdorff fractal dimension of the colony patterns: D(H.Expt)=1.1969 and D(H, R.D.=)1.1965, for experiment and reaction-diffusion model, respectively. Results of our experiments and modeling clearly show how glucose at higher concentration can prove to be inhibitory for motility of growing colonies of B. thuringiensis cells on semisolid support and be responsible for changes in the growth pattern.
[Show abstract][Hide abstract] ABSTRACT: In this article we consider the nonlinear dynamics of domain growth and dynamics under the influence of an external electric field and an intrinsic pinning field due to disorder. The theoretical framework is based on a finite time-difference method as applied to a time-dependent Ginzburg–Landau–Devonshire equation. The domain growth is seen to be of fractal nature, the fractal dimension of which is in good agreement with experiments. When it comes to dynamics we compute the areal velocity of the domain growth as a function of the applied field and find different regions of the nonlinearities that are also in qualitative agreement with experiments.
[Show abstract][Hide abstract] ABSTRACT: This article summarizes the contribution to the phenomenon of Diamagnetism made by Rudolf Peierls, as Quantum Mechanics was
triumphantly unfolding in the 1930’s.
KeywordsDiamagnetism-boundary effects-dissipation-de Haas-van Alphen oscillations
[Show abstract][Hide abstract] ABSTRACT: In this Brief Report we show how the low-temperature thermodynamics of the dissipative motion of an electron in a magnetic field is sensitive to the nature of the spectral density function, J(omega), of the quantum heat bath. In all cases of couplings considered here the free energy and the entropy of the cyclotron motion of the electron fall off to zero as power law in conformity with the third law of thermodynamics. The power of the power law however depends on the nature of J(omega). We also separately discuss the influence of confinement.
[Show abstract][Hide abstract] ABSTRACT: We present a detailed study of the quantum dissipative dynamics of a charged particle in a magnetic field. Our focus of attention is the effect of dissipation on the low- and high-temperature behaviors of the specific heat at constant volume. After providing a brief overview of two distinct approaches to the statistical mechanics of dissipative quantum systems, viz., the ensemble approach of Gibbs and the quantum Brownian motion approach due to Einstein, we present exact analyses of the specific heat. While the low-temperature expressions for the specific heat, based on the two approaches, are in conformity with power-law temperature dependence, predicted by the third law of thermodynamics, and the high-temperature expressions are in agreement with the classical equipartition theorem, there are surprising differences between the dependencies of the specific heat on different parameters in the theory, when calculations are done from these two distinct methods. In particular, we find puzzling influences of boundary confinement and the bath-induced spectral cutoff frequency. Further, when it comes to the issue of approach to equilibrium, based on the Einstein method, the way the asymptotic limit (t-->infinity) is taken seems to assume significance.
[Show abstract][Hide abstract] ABSTRACT: A Landau-like theory of phase transition and its time-dependent generalization are shown to be sufficient for describing the formation and kinetics of 180°, 90°, and vortex (toroidal) domains in ferroelectric thin films. The theory relies only on the choice of boundary conditions and does not require at the outset the presence of either anisotropy or strain fields. An ingredient in the calculational scheme is the incorporation of finite element methods in the kinetic equations for the ferroelectric order parameter.
[Show abstract][Hide abstract] ABSTRACT: A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix $\rho$ of an electron which starts in some coherent state on the qubit. At infinite time, $\rho$ usually approaches the fully decoherent state, with $\rho^{}_{nm}=\delta^{}_{nm}/3$. However, when the Hamiltonian is symmetric under $1\leftrightarrow 2$, the element $\rho^{}_{12}$ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on ${\rm Re}[\rho^{}_{12}(t=0)]$. In several cases, the information stored on the qubit is protected from the noise. Comment: 4 pages, 2 figures
[Show abstract][Hide abstract] ABSTRACT: In this work, low temperature thermodynamic behaviour in the context of dissipative diamagnetism with anomalous coupling is analyzed. We find that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behaviour at low temperature. For Ohmic bath, entropy vanishes linearly with temperature, $T$, in conformity with Nernst's theorem. It is also shown that entropy decays faster in the presence of anomalous coupling than that of the usual coordinate-coordinate coupling. It is observed that velocity-velocity coupling is the most advantageous coupling scheme to ensure the third law of thermodynamics. It is also revealed that different thermodynamic functions are independent of magnetic field at very low temperature for various coupling schemes discussed in this work.
[Show abstract][Hide abstract] ABSTRACT: We revisit here the effect of quantum dissipation on the much studied problem of Landau diamagnetism and analyze the results in the light of the third law of thermodynamics. The case of an additional parabolic potential is separately assessed. We find that dissipation arising from strong coupling of the system to its environment qualitatively alters the low-temperature thermodynamic attributes such as the entropy and the specific heat.
[Show abstract][Hide abstract] ABSTRACT: This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the
problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza
Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results
are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic
fields.
[Show abstract][Hide abstract] ABSTRACT: The “spring-defect model” developed by us earlier to discuss ferroelasticity, exhibited in the orthorhombic phase of YBa2Cu3O7–δ (Y-Ba–Cu–O), is used to analyze anelastic relaxation around the paraelastic to ferroelastic phase transition under the influence of an external inhomogeneous stress. The kinetics of the underlying Hamiltonian representing strain-strain interactions is treated within mean-field theory. The relaxation-response relation of linear response theory is employed to derive explicit expressions for the anelastic strain, the frequency-dependent compliance and the internal friction in terms of the basic parameters of the spring-defect model.
[Show abstract][Hide abstract] ABSTRACT: A spring-defect model has been developed by us earlier for describing the connection between elastic distortion and oxygen ordering and the concomitant structural phase transition (from tetragonal to orthorhombic at Ts900 K) in the high Tc ( 90 K) superconductor YBa2Cu3O7–δ (Y-Ba-Cu-O). This model is used to discuss ferroelasticity, exhibited in the orthorhombic phase of Y-Ba-Cu-O. Ferroelasticity is shown to be a consequence of the interaction between elastic (Zener) dipoles, formed around each oxygen defect. The effective Ising interaction between the defects mediated by host springs, derived earlier, can be recast in the equivalent form of a strain-strain interaction. This form is eminently suitable for discussing the paraelastic to ferroelastic transition, temperature dependence of the ferroelastic order parameter and the static compliance. Results for these quantities, obtained in mean field theory, are presented. The notable feature of this work is not only a derivation of the defect-defect interaction, but also an explicit calculation of the strain dipole tensor associated with each defect, from a microscopic model.
[Show abstract][Hide abstract] ABSTRACT: The slow dynamics and concomitant memory (aging) effects seen in nanomagnetic systems are analyzed on the basis of two separate paradigms: superparamagnets and spin glasses. It is argued that in a large class of aging phenomena it suffices to invoke superparamagnetic relaxation of individual single domain particles but with a distribution of their sizes. Cases in which interactions and randomness are important in view of distinctive experimental signatures are also discussed.
Physical Review B 06/2006; 74(21). DOI:10.1103/PhysRevB.74.214410 · 3.74 Impact Factor