arXiv subjects

Malay Bandyopadhyay

Publications and source records attributed to Malay Bandyopadhyay.

47 records · Page 3Linked to original sources

arXiv2010

DNA breathing dynamics: Analytic results for distribution functions of relevant Brownian functionals

We investigate DNA breathing dynamics by suggesting and examining several different Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size $x_0$, we derive analytical expressions for (i) the distribution $P(t_f|x_0)$ of the first-passage time $t_f$, characterizing the bubble lifetime, (ii) the distribution $P(A|x_0)$ of the area $A$ till the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution $P(M)$ of the maximum bubble size $M$ attained before the first-passage time, and (iv) the joint probability distribution $P(M,t_m)$ of the maximum bubble size $M$ and the time $t_m$ of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numerical simulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

cond-mat.soft↗

arXiv2009

Nucleation of superconductivity under rapid cycling of electric field

The effect of an externally applied high frequency oscillating electric field on the critical nucleation field of superconductivity in the bulk as well as at the surface of a superconductor is investigated in details in this work. Starting from the linearized time dependent Ginzburg-Landau (TDLG) theory and using the variational principle we have shown the analogy between a quantum harmonic oscillator with that of the nucleation of superconductivity in bulk and a quantum double oscillator with that of the nucleation at the surface of a finite sample. The effective Hamiltonian approach of Cook {\it et al} \cite{cook} is employed to incorporate the effect of an externally applied highly oscillating electric field. The critical nucleation field ratio is also calculated from the ground state energy method. The results obtained from these two approximated theories agree very well with the exact results for the case of undriven system which establishes the validity of these two approximated theories. It is observed that the highly oscillating electric field actually increases the bulk critical nucleation field ($H_{c_2}$) as well as the surface critical nucleation field ($H_{c_3}$) of superconductivity as compared to the case of absence of electric field ($\varepsilon_0=0$). But the externally applied rapidly oscillating electric field accentuates the surface critical nucleation field more than the bulk critical nucleation field i.e. the increase of $H_{c_3}$ is 1.6592 times larger than that of $H_{c_2}$.

cond-mat.supr-con↗

arXiv2009

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

Explicit results for various quantum thermodynamic function (QTF) of a charged magneto-oscillator coupled to a heat bath at arbitrary temperature are demonstrated in this paper. Discernible expressions for different QTF in the two limits of very low and very high temperatures are presented for three popular heat bath models : Ohmic, single relaxation time and blackbody radiation. The central result is that the effect of magnetic field turns out to be important at low temperatures yet crucial at high temperatures. It is observed that the dissipation parameter, $γ$, and the cyclotron frequency, $ω_c$, affect the decaying or rising behaviour of various QTF in just the opposite way to each other at low temperatures. In the high temperature regime, the effect of $γ$ is much pronounced than that of $ω_c$.

cond-mat.mes-hall↗

arXiv2009

Quantum Brownian motion under rapid periodic forcing

We study the steady state behaviour 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, $V_{QD}$, which adds on to the classical result. This is shown using a coherent state representation of bath oscillators. $V_{QD}$ 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.

cond-mat.stat-mech↗

arXiv2009

Dissipative diamagnetism with anomalous coupling and third law

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.

cond-mat.mes-hall↗

arXiv2008

Charged oscillator in a heat bath in the presence of a magnetic field & third law of thermodynamics

The quantum thermodynamic behaviour of a charged oscillator in the presence of a magnetic field and coupled to a heat bath through different coupling schemes is obtained analytically. It is shown that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behaviour at low temperature. For the coordinate-coordinates coupling scheme the low temperature explicit results for the case of Ohmic, exponentially correlated and more generalized heat bath models are derived. In all the above mentioned cases free energy and entropy vanish linearly with temperature ($T$) as $T\to 0$ in conformity with Nernst's theorem. It is seen that coordinate (velocity)-velocities (coordinates) coupling is much more beneficial than the coordinate-coordinates coupling to ensure third law of thermodynamics. The case of radiation heat bath shows $T^3$ decay behaviour for entropy as $T\to 0$. It is observed that at low temperature free energy and entropy decay faster for the velocity-velocities scheme than any other coupling schemes. This implies velocity-velocities coupling scheme is the most advantageous coupling scheme in restoring the third law of thermodynamics. It is shown that the low temperature thermodynamic functions are independent of magnetic field for all the above mentioned cases except the without dissipation case.

cond-mat.stat-mech↗

arXiv2006

Memory in nanomagnetic systems: Superparamagnetism versus Spinglass behavior

The slow dynamics and concomitant memory (aging) effects seen in nanomagnetic systems are analyzed on the basis of two separate paradigms : superparamagnets and spinglasses. 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.

cond-mat.stat-mech↗

arXiv2006

Landau-Drude Diamagnetism: Fluctuation, Dissipation and Decoherence

Starting from a quantum Langevin equation (QLE) of a charged particle coupled to a heat bath in the presence of an external magnetic field, we present a fully dynamical calculation of the susceptibility tensor. We further evaluate the position autocorrelation function by using the Gibbs ensemble approach. This quantity is shown to be related to the imaginary part of the dynamical susceptibility, thereby validating the fluctuation-dissipation theorem in the context of dissipative diamagnetism. Finally we present an overview of coherence-to-decoherence transition in the realm of dissipative diamagnetism at zero temperature. The analysis underscores the importance of the details of the relevant physical quantity, as far as coherence to decoherence transition is concerned.

cond-mat.stat-mech↗

arXiv2005

Diffusion Enhancement in a Periodic Potential under High-Frequency Space-Dependent Forcing

We study the long-time behavior of 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 new analysis includes the case when the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of the Kapitsa 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 underdamped Brownian particles in a ratchet potential.

cond-mat.stat-mech↗

arXiv2005

Dissipative Tunneling in 2 DEG: Effect of Magnetic Field, Impurity and Temperature

We have studied the transport process in the two dimensional electron gas (2DEG) in presence of a magnetic field and a dissipative environment at temperature T. By means of imaginary time series functional integral method we calculate the decay rates at finite temperature and in the presence of dissipation. We have studied decay rates for wide range of temperatures -- from the thermally activated region to very low temperature region where the system decays by quantum tunneling. We have shown that dissipation and impurity helps the tunneling. We have also shown that tunneling is strongly affected by the magnetic field. We have demonstrated analytical results for all the cases mentioned above.

cond-mat.stat-mech↗

arXiv2005

Dissipative Diamagnetism -- A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics of Mesoscopic Systems

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.

cond-mat.stat-mech↗