Malay Bandyopadhyay

Memory in nanomagnetic systems : Superparamagnetism versus spin-glass behavior

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.

Coercivity of magnetic nanoparticles: a stochastic model

The variation in magnetic properties with particle size for nanomagnetic particles at 300 K and 10 K has been explained with the help of nonequilibrium statistical mechanics. At room temperature a maximum in the coercivity curve is observed at a critical diameter, dc, so that two different regimes can be distinguished. This clearly indicates two different mechanisms of magnetization reversal as a function of particle size. Using Kramers treatment, the increase in coercivity with an increase in particle size at room temperature in the single-domain region has been clarified. Beyond a certain critical particle size, a multidomain region is formed. Now we invoke supersymmetric quantum mechanics (SUSY QM) for these multi-domain region to explain the decrease in coercivity with an increase in particle size. The decrease in coercivity with an increase in particle size at very low temperature (10 K) is also explained with the help of our two-state model by invoking the concept of effective anisotropy. The variation in the saturation magnetization Ms and the remanence-to-saturation magnetization ratio, Mr Ms, with particle size are discussed in detail. The above results underscore the fact that at room temperature thermal effects dominate, whereas at low temperature (10 K) surface effects govern the magnetization reversal process. In this paper the effect of the magneto-crystalline anisotropic potential on the magnetization of non-interacting uniaxaial nanomagnetic particles is discussed in detail.

Dissipative Diamagnetism—A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics

Using the path integral approach to equilibrium statistical physics the effect of dissipation on Landau diamagnetism is calculated. The calculation clarifies the essential role of the boundary of the container in which the electrons move. Further, the derived result for diamagnetization also matches with the expression obtained from a time-dependent quantum Langevin equation in the asymptotic limit, provided a certain order is maintained in taking limits. This identification then unifies equilibrium and nonequilibrium statistical physics for a phenomenon like diamagnetism, which is inherently quantum and strongly dependent on boundary effects. In addition we have shown that our results are directly connected with fluctuation induced diamagnetic susceptibility of superconducting grains.

Quantum thermodynamics of a charged magneto-oscillator coupled to a heat bath

Explicit results for various quantum thermodynamic functions (QTF) of a charged magneto-oscillator coupled to a heat bath at arbitrary temperature are shown in this paper. Separate expressions for different QTF in the two limits of very low and very high temperatures are presented for three popular heat bath models: the ohmic, single-relaxation-time and black body radiation ones. The central result is that the effect of magnetic field turns out to be important at low temperatures as well as at high temperatures. It is observed that the dissipation parameter, γ, and the cyclotron frequency, ωc, affect the decaying or rising behaviour of various QTF exactly oppositely to each other at low temperatures. In the high temperature regime, the effect of γ is much more pronounced than that of ωc.

Diffusion enhancement in a periodic potential under high-frequency space-dependent forcing.

We study the long-time behavior of an underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time window wherein the effect of frequency-dependent forcing can be replaced by a static effective potential. Our analysis includes the case in which the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of our analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient (D) for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of D due to the space-dependent forcing terms. In addition, we study the transport property (current) of an underdamped Brownian particle in a ratchet potential.

Quantum Brownian motion under rapid periodic forcing

We study the steady state behavior of a confined quantum Brownian particle subjected to a space dependent, rapidly oscillating time-periodic force. To leading order in the period of driving, the result of the oscillating force is an effective static potential which has a quantum dissipative contribution, VQD, which adds on to the classical result. This is shown using a coherent state representation of bath oscillators. VQD is evaluated exactly in the case of an Ohmic dissipation bath. It is strongest for intermediate values of the damping, where it can have pronounced effects.

Magnetic and caloric properties of magnetic nanoparticles: an equilibrium study

The static or thermal equilibrium properties of non-interacting magnetically anisotropic nanoparticles are studied in the framework of classical theory. Various important thermal equilibrium properties, e.g. internal energy, specific heat, magnetization and susceptibility, are derived from basic thermodynamic functions such as the partition function and thermodynamic potentials. The central issue in this paper is to study the effect of anisotropic potential on these thermal equilibrium properties. We extensively study the linear and nonlinear susceptibilities and their temperature dependence. We also give a comparative study of the magnetic properties of a superparamagnetic fine particle system and a canonical spin-glass system and thus invoke the similarities and differences between the two.

Order-parameter scaling in fluctuation-dominated phase ordering.

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile, which capture the breakup and remerging of particle-rich regions. We study both static and dynamic scaling laws obeyed by the Fourier modes Q_{mL} and find that the mean value obeys the static scaling law 〈Q_{mL}〉∼L^{-ϕ}f(m/L) with ϕ≃2/3 and ϕ≃3/5 for Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution, respectively, and ϕ≃3/4 for the CD model. The full probability distribution P(Q_{mL}) exhibits scaling as well. Further, time-dependent correlation functions such as the steady-state autocorrelation and cross-correlations of order-parameter components are scaling functions of t/L^{z}, where L is the system size and z is the dynamic exponent, with z=2 for EW and z=3/2 for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and the weak divergence of the flatness as the scaled time approaches 0.

Zeno and anti-Zeno effects in a dissipative quantum Brownian oscillator model

The purpose of this paper is to investigate the occurrence of the Zeno and anti-Zeno effects for the quantum Brownian motion of a harmonic oscillator. We show a controlled decay suppression and decay acceleration for a dissipative quantum harmonic oscillator. We demonstrate that the system–bath coupling parameter as well as the confining potential can critically control the Zeno and anti-Zeno dynamics. In this context, we discuss several heat bath models such as ohmic, Drude, and the black body radiation model.

Memory effects in the transport properties of a charged magneto-oscillator in a heat bath

In this paper, the cyclotron motion of a charged harmonic oscillator in contact with a dissipative heat bath is considered. Exact results for the ac conductivity are presented for three popular models: Ohmic, Drude and blackbody radiation heat bath models. Significant differences compared to the no memory results are observed in the real and imaginary parts of the ac conductivity tensor due to the presence of non-Markovian (memory) terms and magnetic field. It is seen that the resonant behavior is solely modified by the magnetic field. Interesting interplay between dissipation and magnetic field in changing the line shape of absorption (real part of ac conductivity) and emission (imaginary part of ac conductivity) lines is demonstrated in this work.