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Abhishek Dhar

Publications and source records attributed to Abhishek Dhar.

At least 163 records · Page 9Linked to original sources
arXiv2004

Dynamics of Vibrated Grains

We study number density distribution and the behavior of time correlation functions in the density of grains for a quasi-two dimensional system of vibrated grains. We study the system at various packing fractions, from low to high. At low densities we recover usual gas like behavior, reflected in a Poissonian statistics for the number density distribution. At higher densities we notice effects like formation of cages of the kind that are seen in glass transition.

cond-mat.soft↗
arXiv2004

Work distribution functions in polymer stretching experiments

We compute the distribution of the work done in stretching a Gaussian polymer, made of N monomers, at a finite rate. For a one-dimensional polymer undergoing Rouse dynamics, the work distribution is a Gaussian and we explicitly compute the mean and width. The two cases where the polymer is stretched, either by constraining its end or by constraining the force on it, are examined. We discuss connections to Jarzynski's equality and the fluctuation theorems.

cond-mat.stat-mech↗
arXiv2003

Return to return point memory

We describe a new class of systems exhibiting return point memory (RPM) that are different from those discussed before in the context of ferromagnets. We show numerically that one dimensional random Ising antiferromagnets have RPM, when configurations evolve from a large field. However, RPM is violated when started from some stable configurations at finite field unlike in the ferromagnetic case. This implies that the standard approach to understanding ferromagnetic RPM systems will fail for this case. We also demonstrate RPM with a set of variables that keep track of spin flips at each site. Conventional RPM for the spin configuration is a projection of this result, suggesting that spin flip variables might be a more fundamental representation of the dynamics. We also present a mapping that embeds the antiferromagnetic chain in a two dimensional ferromagnetic model, and prove RPM for spin exchange dynamics in the interior of the chain with this mapping.

cond-mat.stat-mech↗
arXiv2003

Reexamination of experimental tests of the fluctuation theorem

The Fluctuation Theorem and the Jarzynski equality are examined in the light of recent experimental tests. For a particle dragged through a solvent, it is shown that $Q,$ the heat exchanged with the reservoir, obeys the asymptotic Fluctuation Theorem but not the Jarzynski equality, due to slowly decaying tails in its distribution. For molecular stretching experiments, substantial corrections to the Jarzynski equality can result from not measuring the force at the end of the molecule that is moved. We also present a proof of the Fluctuation Theorem for Langevin dynamics that is considerably simpler than the standard proof.

cond-mat.stat-mech↗
arXiv2003

Exact result for nonreciprocity in one-dimensional wave transmission

For sound waves impinging on a one-dimensional medium, we show that nonlinearity can lead to nonreciprocal transmission, without dissipation or broken time reversal invariance. Placing quasi-monochromatic filters at the ends of the nonlinear medium, nonreciprocity can be obtained without the generation of higher harmonics outside the medium. Remarkably, in this configuration the nonreciprocity is found to be proportional to the net energy flow when monochromatic sources of equal strength (at the filter frequency) are simultaneously turned on at both ends. This result is conjectured to be general for one dimensional scattering. It is also shown that although simultaneous monochromatic sources lead to net energy flow, with sources of small but non-zero bandwidth there is no net energy transport, in accordance with the second law of thermodynamics.

cond-mat↗
arXiv2003

Quantum transport using the Ford-Kac-Mazur formalism

The Ford-Kac-Mazur formalism is used to study quantum transport in (1) electronic and (2) harmonic oscillator systems connected to general reservoirs. It is shown that for non-interacting systems the method is easy to implement and is used to obtain many exact results on electrical and thermal transport in one-dimensional disordered wires. Some of these have earlier been obtained using nonequilibrium Green function methods. We examine the role that reservoirs and contacts can have on determining the transport properties of a wire and find several interesting effects.

cond-mat.mes-hall↗
arXiv2003

Ensemble dependence in the Random transverse-field Ising chain

In a disordered system one can either consider a microcanonical ensemble, where there is a precise constraint on the random variables, or a canonical ensemble where the variables are chosen according to a distribution without constraints. We address the question as to whether critical exponents in these two cases can differ through a detailed study of the random transverse-field Ising chain. We find that the exponents are the same in both ensembles, though some critical amplitudes vanish in the microcanonical ensemble for correlations which span the whole system and are particularly sensitive to the constraint. This can \textit{appear} as a different exponent. We expect that this apparent dependence of exponents on ensemble is related to the integrability of the model, and would not occur in non-integrable models.

cond-mat.dis-nn↗
arXiv2003

Isospectrality in Chaotic Billiards

We consider a modification of isospectral cavities whereby the classical dynamics changes from pseudointegrable to chaotic. We construct an example where we can prove that isospectrality is retained. We then demonstrate this explicitly in microwave resonators.

nlin.CD↗
arXiv2003

Heat transport in disordered quantum harmonic oscillator chains

We study heat conduction in quantum disordered harmonic chains connected to general heat reservoirs which are modeled as infinite collection of oscillators. Formal exact expressions for the thermal current are obtained and it is shown that, in some special cases, they reduce to Landauer-like forms. The asymptotic system size dependence of the current is analysed and is found to be similar to the classical case. It is a power law dependence and the power depends on the spectral properties of the reservoirs.

cond-mat.mes-hall↗
arXiv2002

Hidden symmetries in deformed microwave resonators

We explain the ``Hidden symmetries'' observed in wavefunctions of deformed microwave resonators in recent experiments.We also predict that other such symmetries can be seen in microwave resonators.

quant-ph↗
arXiv2002

Triple minima in free energy of semiflexible polymers

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness for finite chains of length L. We find that the polymer properties obtained in this ensemble are "qualitatively" different from those obtained using constant-force ensembles. In particular we find that as we change the stiffness parameter, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.

cond-mat.soft↗
arXiv2002

Comment on ``A simple one-dimensional model of heat conduction which obeys Fourier's law''

A finite Green-Kubo thermal conductivity in a one-dimensional momentum conserving system was reported recently by Garrido et al [Phys. Rev. Lett., vol. 86, 5486 (2001)]. We first comment on the apparent contradiction with an earlier result of Prosen and Campbell [Phys. Rev. Lett., vol. 84, 2857 (2000)]. We then point out certain inconsistencies in their results and disagreements with our own results.

cond-mat.stat-mech↗
arXiv2001

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.

quant-ph↗
arXiv2001

Comment on ``Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?''

In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.

cond-mat.stat-mech↗
arXiv2001

Heat conduction in the disordered harmonic chain revisited

A general formulation is developed to study heat conduction in disordered harmonic chains with arbitrary heat baths that satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat current J is obtained, from which its asymptotic system-size (N) dependence is extracted. It is shown that the ``thermal conductivity'' depends not just on the system itself but also on the spectral properties of the fluctuation and noise used to model the heat baths. As special cases of our heat baths we recover earlier results which reported that for fixed boundaries $J \sim 1/N^{3/2}$, while for free boundaries $J \sim 1/N^{1/2}$. For other choices we find that one can get other power laws including the ``Fourier behaviour'' $J \sim 1/N$.

cond-mat.stat-mech↗
arXiv2001

Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses

We study the nonequlibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from it. Extensive numerical simulations for the two-mass problem indicate that even for arbitrarily small mass differences, a nontrivial steady state is obtained. This state exhibits local thermal equilibrium and has a temperature profile in accordance with the predictions of kinetic theory. The temperature jumps typically seen in such studies are shown to be finite-size effects. The thermal conductivity appears to have a very slow divergence with system size, different from that seen in most other systems.

cond-mat.stat-mech↗
arXiv2001

Solution of a Generalized Stieltjes Problem

We present the exact solution for a set of nonlinear algebraic equations $\frac{1}{z_l}= πd + \frac{2 d}{n} \sum_{m \neq l} \frac{1}{z_l-z_m}$. These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain \cite{dhar}. These equations are low $d$ (density) ``degenerations'' of more complicated transcendental equation of Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, $x_l = \sum_{m \neq l} 1/(x_l-x_m)$, familiar from Random Matrix theory. It is shown that the solutions of these set of equations is given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a ``Green's function'' and a saddle point technique we determine the asymptotic distribution of zeros.

cond-mat↗