arXiv subjects

K. A. Muttalib

Publications and source records attributed to K. A. Muttalib.

At least 19 recordsLinked to original sources

arXiv2026

Phonons in low-dimensional confined systems: Emergent non-reciprocity in 1D

An important feature of solid-state or cold atom systems in low dimensions is the restricted oscillations of ionic/atomic degrees of freedom in the confining directions, for which the conventional phonon from canonical quantization is not an ideal description. In this work we propose a general recipe to introduce this feature to otherwise unrestricted systems by mapping displacement fields to spin degrees of freedom. We demonstrate the validity of the approach with a 1D harmonic chain, and the results lead to massive Dirac fermions at long distances, showing the absence of acoustic modes as the signature of confined out-of-plane motion of the entire chain. We then introduce a short-range interaction via anharmonicities and show that for energy scale slightly above the gap, it gives rise to a (quantum) phase transition to a nonreciprocal state with spontaneous time reversal symmetry breaking (TRSB) of the type $\hat{T}^2=+1$. Despite the non-conserved total particle number, the model holds an under-appreciated $U(1)$ symmetry with conserved "polarization charge", so that the nonreciprocity can be probed by measuring the change of inductivity to artificial gauge fields in and out of the ordered phase.

cond-mat.mes-hall↗

arXiv2025

Temperature inhomogeneity in non-equilibrium field theory for electrons in a nanowire: thermodynamic and transport properties

A nanowire with its two ends fixed at two different temperatures by external baths is the simplest example of a fermionic system with a temperature inhomogeneity, and could be an easy platform to study thermodynamic and transport properties of a boundary-driven open quantum system. Starting with a temperature-dependent pseudo free energy derived from an exact reduced density matrix and assuming a small temperature gradient $γ$ across the wire, we show within perturbation theory that electron dispersion relation and therefore the Fermi distribution becomes $γ$ and space coordinates dependent, leading to non-linear effects of the temperature inhomogeneity. In particular, we show that in the non-linear response regime, the Widemann-Franz Law for the ratio of thermal and electrical conductivities is generalized, and that the thermopower increases with increasing temperature gradient $γ$.

cond-mat.mes-hall↗

arXiv2025

Non-equilibrium field theory with a temperature gradient: Thermal current in a nanowire

A perturbative framework is developed within the standard non-equilibrium field theory techniques to incorporate a temperature gradient across a thermoelectric device. The framework uses a temperature-dependent pseudo-Hamiltonian generated from the exact density matrix in the presence of non-uniform temperatures. We develop a perturbation theory for small temperature gradients in long wires and obtain the non-linear thermal conductance as a function of temperature difference. The framework should be adaptable to more general cases of temperature inhomogeneities in either fermionic or bosonic systems.

cond-mat.mes-hall↗

arXiv2021

Nonmonotonic confining potential and eigenvalue density transition for generalized random matrix model

We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent $γ$ (called the $γ$-ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with $γ=1$ (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the $γ$-ensembles. It enables us to numerically compute the eigenvalue density of $γ$-ensembles for all $γ> 0$. We show that one important effect of the two-particle interaction parameter $γ$ is to generate or enhance the non-monotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing $γ$ can lead to a large non-monotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of $γ$-ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.

cond-mat.dis-nn↗

arXiv2020

On the computation of density and two-point correlation functions of a class of random matrix ensembles

We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a variety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $γ$-ensemble for which analytic results are not yet available.

math-ph↗

arXiv2019

Generalized random matrix model with additional interactions

We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $γ$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem associated with the ensemble. The effect of the additional parameter $γ$ associated with the two-body interaction can be understood in terms of an effective $γ$-dependent single-particle confining potential.

cond-mat.dis-nn↗

arXiv2019

Non-equilibrium phonon transport in surface-roughness dominated nanowires

Experimental observation of highly reduced thermal conductivity in surface-roughness dominated silicon nanowires have generated renewed interest in low-dimensional thermoelectric devices. Using a previous work where the scattering of phonons from a rough surface is mapped to scattering from randomly situated localized phonons in the bulk of a smooth nanowire, we consider the thermal current across a nanowire for various strengths of surface disorder. We use non-equilibrium Green's function techniques that allow us to evaluate the thermal current beyond the linear response regime, for arbitrary cold and hot temperatures of the two semi-infinite connecting leads. We show how the surface-roughness affects the frequency dependence of the thermal current, eventually leading to a temperature dependent reduction of the net current at high temperatures. We use a universal disorder parameter to describe the surface-roughness as has been proposed, and show that the dependence of the net current on this parameter provides a natural explanation for the experimentally observed differences between smooth vs rough surfaces. We argue that a systematic study of the thermal current for different values of the temperature difference between the two sides of a surface-roughness dominated nanowire for various strengths of disorder would help in our understanding of how best to optimize the thermoelectric efficiency.

cond-mat.mes-hall↗

arXiv2019

Phonon localization in surface-roughness dominated nanowires

Studies of possible localization of phonons in nanomaterials have gained importance in recent years in the context of thermoelectricity where phonon-localization can reduce thermal conductivity, thereby improving the efficiency of thermoelectric devices. However, despite significant efforts, phonon-localization has not yet been observed experimentally in real materials. Here we propose that surface-roughness dominated nanowires are ideal candidates to observe localization of phonons, and show numerically that the space and time evolution of the energy generated by a heat-pulse injected at a given point shows clear signatures of phonon localization. We suggest that the same configuration might allow experimental observation of localization of phonons. Our results confirm the universality in the surface-roughness dominated regime proposed earlier, which allows us to characterize the strength of disorder by a single parameter combining the width of the wire as well as the mean height of the corrugation and its correlation length.

cond-mat.mes-hall↗

arXiv2018

Universality of phonon transport in surface-roughness dominated nanowires

We analyze, both theoretically and numerically, the temperature dependent thermal conductivity \k{appa} of two-dimensional nanowires with surface roughness. Although each sample is characterized by three independent parameters - the diameter (width) of the wire, the correlation length and strength of the surface corrugation - our theory predicts that there exists a universal regime where \k{appa} is a function of a single combination of all three model parameters. Numerical simulations of propagation of acoustic phonons across thin wires confirm this universality and predict a d 1/2 dependence of \k{appa} on the diameter d.

cond-mat.dis-nn↗

arXiv2017

Suppressing phonon transport in nanowires: a simple model for phonon-surface roughness interaction

Suppressing phonon propagation in nanowires is an essential goal towards achieving efficient thermoelectric devices. Recent experiments have shown unambiguously that surface roughness is a key factor that can reduce the thermal conductivity well below the Casimir limit in thin crystalline silicon nanowires. We use insights gained from the experimental studies to construct a simple analytically tractable model of the phonon-surface roughness interaction that provides a better theoretical understanding of the effects of surface roughness on the thermal conductivity, which could potentially help in designing better thermoelectric devices.

cond-mat.mes-hall↗

arXiv2013

Non-linear thermoelectric transport: A class of nano-devices for high efficiency and large power output

Molecular junctions and similar devices described by an energy dependent transmission coefficient can have a high linear response thermoelectric figure of merit. Since such devices are inherently non-linear, the full thermodynamic efficiency valid for any temperature and chemical potential difference across the leads is calculated. The general features in the energy dependence of the tranmission function that lead to high efficiency and also high power output are determined. It is shown that the device with the highest efficiency does not necessarily lead to large power output. To illustrate this, we use a model called the t-stub model representing tunneling through an energy level connected to another energy level. Within this model both high efficiency and high power output are achievable. Futhermore, by connecting many nanodevices it is shown to be possible to scale up the power output without compromising efficiency in an (exactly solvable) n-channel model even with tunneling between the devices.

cond-mat.mes-hall↗

arXiv2013

The Generalized DMPK equation revisited: A systematic derivation

The Generalized Dorokov-Mello-Pereyra-Kumar (DMPK) equation has recently been used to obtain a family of very broad and highly asymmetric conductance distributions for three dimensional disordered conductors. However, there are two major criticisms of the derivation of the Generalized DMPK equation: (1) certain eigenvector correlations were neglected based on qualitative arguments that can not be valid for all disorder, and (2) the repulsion between two closely spaced eigenvalues were not rigorously governed by symmetry considerations. In this work we show that it is possible to address both criticisms by including the eigenvalue and eigenvector correlations in a systematic and controlled way. It turns out that the added correlations determine the evolution of the Jacobian, without affecting the evaluation of the conductance distributions. They also guarantee the symmetry requirements. In addition, we obtain an exact relationship between the eigenvectors and the Lyapunov exponents leading to a sum rule for the latter at all disorder.

cond-mat.str-el↗

arXiv2012

Scale-dependent correction to the dynamical conductivity of a disordered system at unitary symmetry

Anderson localization has been studied extensively for more than half a century. However, while our understanding has been greatly enhanced by calculations based on a small epsilon expansion in d = 2 + epsilon dimensions in the framework of non-linear sigma models, those results can not be safely extrapolated to d = 3. Here we calculate the leading scale-dependent correction to the frequency-dependent conductivity sigma(omega) in dimensions d <= 3. At d = 3 we find a leading correction Re{sigma(omega)} ~ |omega|, which at low frequency is much larger than the omega^2 correction deriving from the Drude law. We also determine the leading correction to the renormalization group beta-function in the metallic phase at d = 3.

cond-mat.dis-nn↗

arXiv2010

Universality of a family of Random Matrix Ensembles with logarithmic soft-confinement potentials

Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $λ$ describing logarithmic soft-confinement potentials $V(H) \sim [\ln H]^{(1+λ)} \:(λ>0$). We showed that we can study eigenvalue correlations of these "$λ$-ensembles" based on the numerical construction of the corresponding orthogonal polynomials with respect to the weight function $\exp[- (\ln x)^{1+λ}]$. In this work, we expand our previous work and show that: i) the eigenvalue density is given by a power-law of the form $ρ(x) \propto [\ln x]^{λ-1}/x$ and ii) the two-level kernel has an anomalous structure, which is characteristic of the critical ensembles. We further show that the anomalous part, or the so-called "ghost-correlation peak", is controlled by the parameter $λ$; decreasing $λ$ increases the anomaly. We also identify the two-level kernel of the $λ$-ensembles in the semiclassical regime, which can be written in a sinh-kernel form with more general argument that reduces to that of the critical ensembles for $λ=1$. Finally, we discuss the universality of the $λ$-ensembles, which includes Wigner-Dyson universality ($λ\to \infty$ limit), the uncorrelated Poisson-like behavior ($λ\to 0$ limit), and a critical behavior for all the intermediate $λ$ ($0<λ<\infty$) in the semiclassical regime. We also comment on the implications of our results in the context of the localization-delocalization problems as well as the $N$ dependence of the two-level kernel of the fat-tail random matrices.

cond-mat.dis-nn↗

arXiv2010

Two-level correlation function of $λ$-ensembles

Recently we introduced a family of U(N) invariant random matrix ensembles which is a one-paramter ($λ$) extension of the q-random matrix ensembles (RMEs), given by the asymptotic weak confining potential $V(H) \sim [\ln H]^{(1+λ)}$ \cite{cm-jpa09}. With numerical construction of the corresponding orthogonal polynomials, we showed that the eigenvalue density of the ensembles deviates from the inverse power law and that the two-level kernel of the ensembles is qualitatively different from those of Gaussian and the critical ensembles. In this work, we make further efforts to characterize the two-level kernel of the $λ$-ensembles and discuss its various properties. To this end, we first show that the kernel of the $λ$-ensembles also possess an anomalous structure characteristic of the critical ensembles, namely the ghost correlation peak. We then propose, albeit in a restricted regime, a form of the two-level kernel which is distinct from the sine kernel of the Gaussian ensembles as well as the sinh kernel of the critical ensembles. We test the proposed form numerically and discuss its implications. In particular, we show that the case $λ> 1$ is qualitatively distinct from the case $λ<1$, the latter decribing true fat-tail ensembles.

cond-mat.stat-mech↗

arXiv2010

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation on the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b approximately 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin wave excitations renders the dephasing length L_phi < b in the range of sheet resistances considered, so that the effective dimension is d = 3. The observed approximate fractional temperature power law of the conductivity is ascribed to the scaling regime near the transition. The conductivity data as a function of temperature and disorder strength collapse on to two scaling curves for the metallic and insulating regimes. The best fit is obtained for a dynamical exponent z approximately 2.5 and a correlation length critical exponent ν' approximately 1.4 on the metallic side and a localization length exponent νapproximately 0.8 on the insulating side.

cond-mat.dis-nn↗

arXiv2009

Distribution of conductance for Anderson Insulators: A theory with a single parameter

We obtain an analytic expression for the full distribution of conductance for a strongly disordered three dimensional conductor within a perturbative approach based on the transfer-matrix formulation. Our results confirm numerical evidence that the log-normal limit of the distribution is not reached even in the deeply insulating regime. We show that the variance of the logarithm of the conductance scales as a fractional power of the mean, while the skewness changes sign as one approaches the Anderson metal-insulator transition from the deeply insulating limit, all described as a function of a single parameter. The approach suggests a possible single parameter description of the Anderson transition that takes into account the full nontrivial distribution of conductance.

cond-mat.dis-nn↗

arXiv2009

Rotationally invariant family of Lévy like random matrix ensembles

We introduce a family of rotationally invariant random matrix ensembles characterized by a parameter $λ$. While $λ=1$ corresponds to well-known critical ensembles, we show that $λ\ne 1$ describes "Lévy like" ensembles, characterized by power law eigenvalue densities. For $λ> 1$ the density is bounded, as in Gaussian ensembles, but $λ<1$ describes ensembles characterized by densities with long tails. In particular, the model allows us to evaluate, in terms of a novel family of orthogonal polynomials, the eigenvalue correlations for Lévy like ensembles. These correlations differ qualitatively from those in either the Gaussian or the critical ensembles.

cond-mat.stat-mech↗