arXiv subjects

Alex Kamenev

Publications and source records attributed to Alex Kamenev.

At least 91 records · Page 5Linked to original sources

arXiv2008

Population extinction in a time-modulated environment

The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent branching rate. The population extinction is treated in eikonal approximation, where it is described as an instanton trajectory of a proper reaction Hamiltonian. The modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase. We calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations. The techniques include a first-order theory with respect to the modulation amplitude, a second-order theory in the spirit of the Kapitsa pendulum effect, and adiabatic theory valid for low modulation frequencies.

cond-mat.stat-mech↗

arXiv2008

Population extinction in a fluctuating environment

Environmental noise can cause an exponential reduction in the mean time to extinction (MTE) of an isolated population. We study this effect on an example of a stochastic birth-death process with rates modulated by a colored Gaussian noise. A path integral formulation yields a transparent way of evaluating the MTE and finding the optimal realization of the environmental noise that determines the most probable path to extinction. The population-size dependence of the MTE changes from exponential in the absence of the environmental noise to a power law for a short-correlated noise and to no dependence for long-correlated noise. We also establish the validity domains of the limits of white noise and adiabatic noise.

q-bio.PE↗

arXiv2008

Extinction of an infectious disease: a large fluctuation in a non-equilibrium system

We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in conjunction with the eikonal approximation. In this way the problem is reduced to finding the optimal path to extinction: a heteroclinic trajectory of an effective multi-dimensional classical Hamiltonian system. We compute this trajectory and mean extinction time of the disease numerically and uncover a non-monotone, spiral path to extinction of a disease. We also obtain analytical results close to a bifurcation point, where the problem is described by a Hamiltonian previously identified in one-species population models.

cond-mat.stat-mech↗

arXiv2007

Coulomb drag at zero temperature

We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet conductance. The effect is therefore the strongest in low mobility samples. This behavior should be contrasted with the conventional (second order) prediction that the transresistance scales as a certain power of temperature and is almost mobility-independent. The result demonstrates that the zero-temperature drag is not an unambiguous signature of a strongly-coupled state in double-layer systems.

cond-mat.mes-hall↗

arXiv2007

Singular length dependence of critical current in SNS bridges

We examine dependence of the critical Josephson current on the length L of the normal bridge N between two bulk superconductors. This dependence turns out to be nonanalytic at small L. The nonanalyticity originates from the contribution of extended quasiparticle states with energies well above the superconducting gap. This should be contrasted with the more familiar contribution to the Josephson current coming from Andreev bound states localized in the normal region at energies below the gap.

cond-mat.supr-con↗

arXiv2007

Keldysh Ginzburg-Landau action of fluctuating superconductors

We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $Δ$-dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor'kov-Eliashberg coupling between $Δ$ and the scalar potential, as well as a peculiar nonlocal nonlinear term. The action is gauge invariant and satisfies the fluctuation dissipation theorem. It may be employed e.g. for calculation of higher moments of the current fluctuations.

cond-mat.supr-con↗

arXiv2007

Zero-bias anomaly in the tunneling density of states of graphene

In the vicinity of the Fermi energy, the band structure of graphene is well described by a Dirac equation. Impurities will generally induce both a scalar potential as well as a (fictitious) gauge field acting on the Dirac fermions. We show that the angular dependence of the zero-bias anomaly in the spatially resolved tunneling density of states (TDOS) around a particular impurity allows one to distinguish between these two contributions. Our predictions can be tested in scanning-tunneling-microscopy measurements on graphene.

cond-mat.mes-hall↗

arXiv2006

Towards Classification of Phase Transitions in Reaction--Diffusion Models

Equilibrium phase transitions are associated with rearrangements of minima of a (Lagrangian) potential. Treatment of non-equilibrium systems requires doubling of degrees of freedom, which may be often interpreted as a transition from the ``coordinate'' to the ``phase'' space representation. As a result, one has to deal with the Hamiltonian formulation of the field theory instead of the Lagrangian one. We suggest a classification scheme of phase transitions in reaction-diffusion models based on the topology of the phase portraits of corresponding Hamiltonians. In models with an absorbing state such a topology is fully determined by intersecting curves of zero ``energy''. We identify four families of topologically distinct classes of phase portraits stable upon RG transformations.

cond-mat.stat-mech↗

arXiv2005

Inelastic electron transport in granular arrays

Transport properties of granular systems are governed by Coulomb blockade effects caused by the discreteness of the electron charge. We show that, in the limit of vanishing mean level spacing on the grains, the low-temperature behavior of 1d and 2d arrays is insulating at any inter-grain coupling (characterized by a dimensionless conductance g.) In 2d and g>>1, there is a sharp Berezinskii-Kosterlitz-Thouless crossover to the conducting phase at a certain temperature, T_{BKT}. These results are obtained by applying an instanton analysis to map the conventional `phase' description of granular arrays onto the dual `charge' representation.

cond-mat.mes-hall↗

arXiv2005

Anderson localization from the replica formalism

We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $σ$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons and Zirnbauer \cite{LSZ}, we compute the {\em exact} density of transmission matrix eigenvalues of superconducting wires (of symmetry class $C$I.) For the unitary class of metallic systems (class $A$) we are able to obtain the density function, save for its large transmission tail.

cond-mat.mes-hall↗

arXiv2005

Many-body theory of non-equilibrium systems

Lectures notes for 2004 Les Houches Summer School on "Nanoscopic Quantum Transport". These lectures contain an introduction to Keldysh formalism for interacting bosonic and fermionic systems, presented in the functional integral framework. Covered topics include: kinetic theory, relation to classical techniques (such as Martin--Siggia--Rose and Fokker--Planck), non--linear sigma model for disordered fermions, etc.

cond-mat.dis-nn↗

arXiv2004

Rare Events Statistics in Reaction--Diffusion Systems

We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian, encoding the system's evolution. To this end we formulate corresponding canonical dynamical system and investigate its phase portrait. The method is presented for a number of pedagogical examples.

cond-mat.stat-mech↗

arXiv2004

Electron transport in two-dimensional arrays

We study charge transport in a granular array with high inter-grain conductances. We show that the system exhibits a Berezinskii-Kosterlitz-Thouless crossover from the high-temperature conducting state into a low-temperature insulating state. The crossover takes place at a critical temperature T_{BKT} \propto E_c exp{-g}, where E_c is the charging energy of a grain and g >> 1 is the dimensionless inter-grain conductance. A uniformly applied gate voltage drives the insulator into a conducting charge liquid state followed by an insulating lattice-pinned Wigner crystal state at larger values of the gate voltage. Technically, we establish correspondence between the charge and phase representations, employing the instanton gas summation in the framework of the phase model.

cond-mat.mes-hall↗

arXiv2003

Electron Transport in Granular Metals

We consider thermodynamic and transport properties of a long granular array with strongly connected grains (inter-grain conductance g>>1.) We find that the system exhibits activated behavior of conductance and thermodynamic density of states ~exp(-T*/T) where the gap, T*, is parametrically larger than the energy at which conventional perturbation theory breaks down. The scale T* represents energy needed to create a long single-electron charge soliton propagating through the array.

cond-mat.mes-hall↗

arXiv2002

Correlation functions of the BC Calogero-Sutherland model

The BC-type Calogero-Sutherland model (CSM) is an integrable extension of the ordinary A-type CSM that possesses a reflection symmetry point. The BC-CSM is related to the chiral classes of random matrix ensembles (RMEs) in exactly the same way as the A-CSM is related to the Dyson classes. We first develop the fermionic replica sigma-model formalism suitable to treat all chiral RMEs. By exploiting ''generalized color-flavor transformation'' we then extend the method to find the exact asymptotics of the BC-CSM density profile. Consistency of our result with the c=1 Gaussian conformal field theory description is verified. The emerging Friedel oscillations structure and sum rules are discussed in details. We also compute the distribution of the particle nearest to the reflection point.

cond-mat.str-el↗

arXiv2001

Numerical study of quasiparticle lifetime in quantum dots

The decay rate of quasiparticles in quantum dots is studied through the real time calculation of the single-particle Green function in the self-consistent approximation. The method avoids exact diagonalization, transforming the problem into a system of coupled non-linear integral equations which may be solved iteratively. That allows us to study systems larger than previously treated in the literature. Our results for the inverse participation ratio of many-body states show that the threshold energy for the quasiparticle disintegration is $E^\ast \sim \sqrt{g} Δ$. The delocalization transition is soft rather than sharp. Three different regimes as function of the effective interaction strength may be clearly identified at high energies.

cond-mat.mes-hall↗

arXiv2001

Keldysh and Doi-Peliti Techniques for out-of-Equilibrium Systems

Lecture notes presented at Windsor NATO school on "Field Theory of Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems" (August 2001). The purpose of these lectures is to give a brief modern introduction to Keldysh non-equilibrium field theory and its classical analog - Doi-Peliti technique. The special emphasis is put on stressing the analogy between the two approaches.

cond-mat.mes-hall↗

arXiv2001

Replica treatment of non-Hermitian disordered Hamiltonians

We employ the fermionic and bosonic replicated nonlinear sigma models to treat Ginibre unitary, symplectic, and orthogonal ensembles of non-Hermitian random matrix Hamiltonians. Using saddle point approach combined with Borel resummation procedure we derive the exact large-N results for microscopic density of states in all three ensembles. We also obtain tails of the density of states as well the two-point function for the unitary ensemble.

cond-mat.dis-nn↗