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K. Mallick

Publications and source records attributed to K. Mallick.

At least 19 recordsLinked to original sources
arXiv2026

The 10-15 GHz radio continuum survey of the Galactic Plane with SKAO

Star formation emerges from the complex interplay between gravity, turbulence, magnetic fields, and stellar feedback, all of which vary across spatial scales and Galactic environments. Over the past decades, extensive multiwavelength surveys of the Galactic Plane have progressively unveiled this complexity. Far-infrared and sub-millimetre surveys have identified and characterized tens of thousands of star-forming regions, revealing their mass, temperature, and evolutionary stage. Complementary molecular-line surveys, spanning several CO transitions and isotopologues, have mapped the gas kinematics from giant molecular clouds down to sub-parsec structures. The advent of interferometers such as ALMA has revolutionized this field, enabling systematic studies of gas dynamics, fragmentation, and collapse in dense clumps at scales of a few thousand astronomical units. At the same time, mid-infrared and radio surveys at frequencies 0.8 <= nu <= 5 GHz have traced ionised gas associated with the earliest and latest phases of massive-star evolution, including thermal radio jets, hypercompact and ultracompact HII regions, supernova remnants, planetary nebulae, and evolved massive stars. Yet, a uniform, Galaxy-wide census of ionised structures and feedback processes remains elusive. A transformational leap forward requires a sensitive, high-resolution radio survey of the Galactic Plane at 10-15 GHz, capable of resolving physical scales smaller than 0.05 pc at distances up to 20 kpc. This is precisely the goal of the SKA-Mid Galactic Plane survey, which will, with its unprecedented sensitivity, angular resolution, and mapping speed, provide the first panoptic view of ionised gas and stellar feedback across the Milky Way.

astro-ph.GA↗
arXiv2019

Semi-classical work and quantum work identities in Weyl representation

We derive a semi-classical nonequilibrium work identity by applying the Wigner-Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us, to the leading order in $\hbar$, to overcome the problem of defining the concept of work in quantum mechanics. We propose a geometric interpretation of this semi-classical relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable case of the quantum harmonic oscillator.

quant-ph↗
arXiv2017

Quantum return probability of a system of $N$ non-interacting lattice fermions

We consider $N$ non-interacting fermions performing continuous-time quantum walks on a one-dimensional lattice. The system is launched from a most compact configuration where the fermions occupy neighboring sites. We calculate exactly the quantum return probability (sometimes referred to as the Loschmidt echo) of observing the very same compact state at a later time $t$. Remarkably, this probability depends on the parity of the fermion number -- it decays as a power of time for even $N$, while for odd $N$ it exhibits periodic oscillations modulated by a decaying power law. The exponent also slightly depends on the parity of $N$, and is roughly twice smaller than what it would be in the continuum limit. We also consider the same problem, and obtain similar results, in the presence of an impenetrable wall at the origin constraining the particles to remain on the positive half-line. We derive closed-form expressions for the amplitudes of the power-law decay of the return probability in all cases. The key point in the derivation is the use of Mehta integrals, which are limiting cases of the Selberg integral.

cond-mat.mes-hall↗
arXiv2017

Large deviations of a tracer in the symmetric exclusion process

The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite lattice with a step initial profile with average densities $ρ_{+}$ and $ρ_{-}$ on the right and on the left of the origin. When $ρ_{+} = ρ_{-}$, the gas is at equilibrium and undergoes stationary fluctuations. When these densities are unequal, the gas is out of equilibrium and will remain so forever. A tracer, or a tagged particle, is initially located at the boundary between the two domains; its position $X_t$ is a random observable in time, that carries information on the non-equilibrium dynamics of the whole system. We derive an exact formula for the cumulant generating function and the large deviation function of $X_t$, in the long time limit, and deduce the full statistical properties of the tracer's position. The equilibrium fluctuations of the tracer's position, when the density is uniform, are obtained as an important special case.

cond-mat.stat-mech↗
arXiv2016

Quantum centipedes: collective dynamics of interacting quantum walkers

We consider the quantum centipede made of $N$ fermionic quantum walkers on the one-dimensional lattice interacting by means of the simplest of all hard-bound constraints: the distance between two consecutive fermions is either one or two lattice spacings. This composite quantum walker spreads ballistically, just as the simple quantum walk. However, because of the interactions between the internal degrees of freedom, the distribution of its center-of-mass velocity displays numerous ballistic fronts in the long-time limit, corresponding to singularities in the empirical velocity distribution. The spectrum of the centipede and the corresponding group velocities are analyzed by direct means for the first few values of $N$. Some analytical results are obtained for arbitrary $N$ by exploiting an exact mapping of the problem onto a free-fermion system. We thus derive the maximal velocity describing the ballistic spreading of the two extremal fronts of the centipede wavefunction, including its non-trivial value in the large-$N$ limit.

cond-mat.stat-mech↗
arXiv2016

Matrix product solution to a 2-species TASEP with open integrable boundaries

We present an explicit representation for the matrix product ansatz for some two-species TASEP with open boundary conditions. The construction relies on the integrability of the models, a property that constrains the possible rates at the boundaries. The realisation is built on a tensor product of copies of the DEHP algebras. Using this explicit construction, we are able to calculate the partition function of the models. The densities and currents in the stationary state are also computed. It leads to the phase diagram of the models. Depending on the values of the boundary rates, we obtain for each species shock waves, maximal current, or low/high densities phases.

cond-mat.stat-mech↗
arXiv2015

Interacting quantum walkers: Two-body bosonic and fermionic bound states

We investigate the dynamics of bound states of two interacting particles, either bosons or fermions, performing a continuous-time quantum walk on a one-dimensional lattice. We consider the situation where the distance between both particles has a hard bound, and the richer situation where the particles are bound by a smooth confining potential. The main emphasis is on the velocity characterizing the ballistic spreading of these bound states, and on the structure of the asymptotic distribution profile of their center-of-mass coordinate. The latter profile generically exhibits many internal fronts.

cond-mat.mes-hall↗
arXiv2015

Inhomogeneous discrete-time exclusion processes

We study discrete time Markov processes with periodic or open boundary conditions and with inhomogeneous rates in the bulk. The Markov matrices are given by the inhomogeneous transfer matrices introduced previously to prove the integrability of quantum spin chains. We show that these processes have a simple graphical interpretation and correspond to a sequential update. We compute their stationary state using a matrix ansatz and express their normalization factors as Schur polynomials. A connection between Bethe roots and Lee-Yang zeros is also pointed out.

cond-mat.stat-mech↗
arXiv2015

Open two-species exclusion processes with integrable boundaries

We give a complete classification of integrable Markovian boundary conditions for the asymmetric simple exclusion process with two species (or classes) of particles. Some of these boundary conditions lead to non-vanishing particle currents for each species. We explain how the stationary state of all these models can be expressed in a matrix product form, starting from two key components, the Zamolodchikov-Faddeev and Ghoshal-Zamolodchikov relations. This statement is illustrated by studying in detail a specific example, for which the matrix Ansatz (involving 9 generators) is explicitly constructed and physical observables (such as currents, densities) calculated.

cond-mat.stat-mech↗
arXiv2014

Survival of classical and quantum particles in the presence of traps

We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative differences in the temporal behavior of the survival probabilities of both kinds of particles. As a general rule, static traps are far less efficient to absorb quantum particles than classical ones. Several lattice geometries are successively considered: an infinite chain with a single trap, a finite ring with a single trap, a finite ring with several traps, and an infinite chain and a higher-dimensional lattice with a random distribution of traps with a given density. For the latter disordered systems, the classical and the quantum survival probabilities obey a stretched exponential asymptotic decay, albeit with different exponents. These results confirm earlier predictions, and the corresponding amplitudes are evaluated. In the one-dimensional geometry of the infinite chain, we obtain a full analytical prediction for the amplitude of the quantum problem, including its dependence on the trap density and strength.

cond-mat.stat-mech↗
arXiv2012

Growth Inside a Corner: The Limiting Interface Shape

We investigate the growth of a crystal that is built by depositing cubes onto the inside of a corner. The interface of this crystal evolves into a limiting shape in the long-time limit. Building on known results for the corresponding two-dimensional system and accounting for the symmetries of the three-dimensional problem, we conjecture a governing equation for the evolution of the interface profile. We solve this equation analytically and find excellent agreement with simulations of the growth process. We also present a generalization to arbitrary spatial dimension.

cond-mat.stat-mech↗
arXiv2011

On stochastic differential equations with random delay

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation with random delay, the corresponding deterministic equation has order $n+1$. We analyze various examples of dynamical systems of this kind, and find a number of unusual behaviors. For instance, for the harmonic oscillator with random delay, the energy grows as $\exp((3/2)\,t^{2/3})$ in reduced units. We then investigate the effect of introducing a discrete time step $ε$. At variance with the continuous situation, the discrete random recursion relations thus obtained have intrinsic fluctuations. The crossover between the fluctuating discrete problem and the deterministic continuous one as $ε$ goes to zero is studied in detail on the example of a first-order linear differential equation.

cond-mat.stat-mech↗
arXiv2011

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

cond-mat.stat-mech↗
arXiv2011

Condensation of actin filaments pushing against a barrier

We develop a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force-velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially, and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.

cond-mat.stat-mech↗
arXiv2010

Modified Fluctuation-dissipation theorem for non-equilibrium steady-states and applications to molecular motors

We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady-states and obeying markovian dynamics. We discuss the interpretation of this result in terms of trajectory entropy excess. The framework is illustrated on a simple pedagogical example of a molecular motor. We also derive in this context generalized Green-Kubo relations similar to the ones derived recently by Seifert., Phys. Rev. Lett., 104, 138101 (2010) for more general networks of biomolecular states.

cond-mat.stat-mech↗
arXiv2010

Fluctuation relations for molecular motors

This review is focused on the application of specific fluctuation relations, such as the Gallavotti-Cohen relation, to ratchet models of a molecular motor. A special emphasis is placed on two-states models such as the flashing ratchet model. We derive the Gallavotti-Cohen fluctuation relation for these models and we discuss some of its implications.

cond-mat.stat-mech↗
arXiv2009

Fluctuation Theorem for the flashing ratchet model of molecular motors

Molecular motors convert chemical energy derived from the hydrolysis of ATP into mechanical energy. A well-studied model of a molecular motor is the flashing ratchet model. We show that this model exhibits a fluctuation relation known as the Gallavotti-Cohen symmetry. Our study highlights the fact that the symmetry is present only if the chemical and mechanical degrees of freedom are both included in the description.

cond-mat.stat-mech↗