arXiv subjects

K. S. Tikhonov

Publications and source records attributed to K. S. Tikhonov.

At least 19 recordsLinked to original sources

arXiv2026

Spin vs. position conjugation in quantum simulations with atoms: application to quantum chemistry

The permutation symmetry is a fundamental attribute of the collective wavefunction of indistinguishable particles. It makes a difference for the behavior of collective systems having different quantum statistics but existing in the same environment. Here we show that for some specific quantum conjugation between the spin and spatial degrees of freedom the indistinguishable particles can behave similarly for either quantum statistics. In particular, a mesoscopically scaled collection of atomic qubits, mediated by optical tweezers, can model the behavior of a valent electronic shell compounded with nuclear centers in molecules. This makes possible quantum simulations of mono and divalent bonds in quantum chemistry by manipulation of up to four bosonic atoms confined with optical microtraps.

quant-ph↗

arXiv2025

Limits of Perturbation Theory for Multimode Light Propagation in Dispersive Optical Cavities

Temporal modes of quantum light pulses is a promising resource for modern quantum technologies, driving advancements in quantum computing, communication, and metrology. Precise control and manipulation of these modes remain critical challenges, particularly in systems where nonlinear multimode dynamics interact with dispersion effects. In this work, we focus on the role of group velocity dispersion (GVD) within optical cavities - a phenomenon traditionally viewed as detrimental but increasingly recognized as a versatile tool for quantum light manipulation. We present a perturbation-theory-based approach to analyze GVD effects in a synchronously pumped dispersive cavity. By comparing perturbative solutions to rigorous steady-state results, we establish the validity region of the perturbative approach and assess its limitations in multimode systems. Our study identifies key parameters governing the breakdown of perturbation theory, such as mode order, dispersion strength, and cavity decay rates.

quant-ph↗

arXiv2024

Local Density of States Correlations in the Lévy-Rosenzweig-Porter random matrix ensemble

We present an analytical calculation of the local density of states correlation function $ β(ω) $ in the Lévy-Rosenzweig-Porter random matrix ensemble at energy scales larger than the level spacing but smaller than the bandwidth. The only relevant energy scale in this limit is the typical level width $Γ_0$. We show that $β(ω\ll Γ_0) \sim W/Γ_0$ (here $W$ is width of the band) whereas $β(ω\gg Γ_0) \sim (W/Γ_0) (ω/Γ_0)^{-μ} $ where $μ$ is an index characterising the distribution of the matrix elements. We also provide an expression for the average return probability at long times: $\ln [R(t\ggΓ_0^{-1})] \sim -(Γ_0 t)^{μ/2}$. Numerical results based on the pool method and exact diagonalization are also provided and are in agreement with the analytical theory.

cond-mat.dis-nn↗

arXiv2022

Coupled dynamics of spin qubits in optical dipole microtraps

Single atoms in dipole microtraps or optical tweezers have recently become a promising platform for quantum computing and simulation. Here we report a detailed theoretical analysis of the physics underlying an implementation of a Rydberg two-qubit gate in such a system -- a cornerstone protocol in quantum computing with single atoms. We focus on a blockade-type entangling gate and consider various decoherence processes limiting its performance in a real system. We provide numerical estimates for the limits on fidelity of the maximally entangled states and predict the full process matrix corresponding to the noisy two-qubit gate. Our methods and results may find implementation in numerical models for simulation and optimization of neutral atom based quantum processors.

quant-ph↗

arXiv2022

The effect of elastic disorder on single electron transport through a buckled nanotube

We study transport properties of a single electron transistor based on elastic nanotube. Assuming that an external compressive force is applied to the nanotube, we focus on the vicinity of the Euler buckling instability. We demonstrate that in this regime the transport through the transistor is extremely sensitive to elastic disorder. In particular, built-in curvature (random or regular) leads to the ``elastic curvature blockade'': appearance of threshold bias voltage in the $I$-$V$ curve which can be larger than the Coulomb-blockade-induced one. In the case of a random curvature, an additional plateau in dependence of the average current on a bias voltage appears.

cond-mat.mes-hall↗

arXiv2021

Entanglement entropy and particle number cumulants of disordered fermions

We study the entanglement entropy and particle number cumulants for a system of disordered noninteracting fermions in $d$ dimensions. We show, both analytically and numerically, that for a weak disorder the entanglement entropy and the second cumulant (particle number variance) are proportional to each other with a universal coefficient. The corresponding expressions are analogous to those in the clean case but with a logarithmic factor regularized by the mean free path rather than by the system size. We also determine the scaling of higher cumulants by analytical (weak disorder) and numerical means. Finally, we predict that the particle number variance and the entanglement entropy are nonanalytic functions of disorder at the Anderson transition.

cond-mat.mes-hall↗

arXiv2021

From Anderson localization on Random Regular Graphs to Many-Body localization

The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the "most long-range" interaction. Central themes -- which are common to the RRG and MBL problems -- include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.

cond-mat.dis-nn↗

arXiv2020

Instantons in the out-of-equilibrium Coulomb blockade

Physical properties of single-electron devices in the week Coulomb blockade regime are significantly dependent on non-perturbative effects. They arise as instanton solutions of equations of motion for the corresponding Ambegaokar-Eckern-Schoen action. In equilibrium those solutions are known as Korshunov instantons. In this paper we study non-equilibrium Ambegaokar-Eckern- Schoen action using Keldysh technique. We found instantons for the most general stationary out-of equilibrium state. We also found that action saddle-point value assumes a universal value irrespective of the stationary non-equilibrium state.

cond-mat.mes-hall↗

arXiv2020

Magnetotransport and internodal tunnelling in Weyl semimetals

Internodal dynamics of quasiparticles in Weyl semimetals manifest themselves in hydrodynamic, transport and thermodynamic phenomena and are essential for potential valleytronic applications of these systems. In an external magnetic field, coherent quasiparticle tunnelling between the nodes modifies the quasiparticle dispersion and, in particular, opens gaps in the dispersion of quasiparticles at the zeroth Landau level. We study magnetotransport in a Weyl semimetal taking into account mechanisms of quasiparticle scattering both affected by such gaps and independent of them. We compute the longitudal resistivity of a disordered Weyl semimetal with two nodes in a strong magnetic field microscopically and demonstrate that in a broad range of magnetic fields it has a strong angular dependence $ρ(η)\propto C_1+C_2 \cos^2η$, where $η$ is the angle between the field and the separation between the nodes in momentum space. The first term is determined by the coherent internodal tunnelling and is important only at angles $η$ close to $π/2$. This contribution depends exponentially on the magnetic field, $\propto \exp\left(-B_0/B\right)$. The second term is weakly dependent on the magnetic field for realistic concentrations of the impurities in a broad interval of fields.

cond-mat.mes-hall↗

arXiv2019

Asymmetry of non-local dissipation: From drift-diffusion to hydrodynamics

We study dissipation in inhomogeneous two-dimensional electron systems. We predict a relatively strong current-induced spatial asymmetry in the heating of the electron and phonon systems -- even if the inhomogeneity responsible for the electrical resistance is symmetric with respect to the current direction. We also show that the heat distributions in the hydrodynamic and impurity-dominated limits are essentially different. In particular, within a wide, experimentally relevant interval of driving fields, the dissipation profile in the hydrodynamic limit turns out to be asymmetric, and the characteristic spatial scale of the temperature distribution can be controlled by the driving field. By contrast, in the same range of parameters, impurity-dominated heating is almost symmetric, with the size of the dissipation region being independent of the field. This allows one to distinguish experimentally the hydrodynamic and impurity-dominated limits. Our results are consistent with recent experimental findings on transport and dissipation in narrow constrictions and quantum point contacts.

cond-mat.mes-hall↗

arXiv2019

Criteria of minimum squeezing for quantum cluster state generation

In this paper, we assess possibilities of generating cluster states with different topologies being possessed of a finite squeezing resource of the initial oscillators used to generate a cluster state. We obtained the condition on minimum squeezing required for generating a cluster with a given topology as a simple estimation in terms of the coefficients of the adjacency matrix

quant-ph↗

arXiv2019

Critical behavior at the localization transition on random regular graphs

We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number $m+1 = 3$, with a box distribution of disorder and in the middle of the band (energy $E=0$), which is the model most frequently considered in the literature. As a first step, we carry out an accurate determination of the critical disorder, with the result $W_c =18.17\pm 0.01$. After this, we determine the dependence of the correlation volume $N_ξ= m^ξ$ (where $ξ$ is the associated correlation length) on disorder $W$ on the delocalized side of the transition, $W < W_c$, by means of population dynamics. The asymptotic critical behavior is found to be $ξ\propto (W_c-W)^{-1/2}$, in agreement with analytical prediction. We find very pronounced corrections to scaling, in similarity with models in high spatial dimensionality and with many-body localization transitions.

cond-mat.dis-nn↗

arXiv2018

SYK model with quadratic perturbations: the route to a non-Fermi-liquid

We study the stability of the SYK$_4$ model with a large but finite number of fermions $N$ with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK$_2$ perturbation and demonstrate the stability of the SYK$_4$ infra-red asymptotic behavior characterized by a Green function $G(τ) \propto 1/τ^{3/2} $, with respect to weak perturbation. This result is supported by exact numerical diagonalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.

cond-mat.str-el↗

arXiv2018

Statistics of eigenstates near the localization transition on random regular graphs

Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes $N$ below the correlation volume $N_ξ$ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length $ξ\sim \log N_ξ$ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast "diffusion" which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance $Σ_2(ω)$ crossing over, with increasing freqyency $ω$, from ergodic behavior $Σ_2=\left(2/π^2\right)\lnω/Δ$ to $Σ_2\propto ω^2$ at $ω_c\sim (N N_ξ)^{-1/2}$ and finally to Poissonian behavior $Σ_2 = ω/Δ$ at $ω_ξ\sim N_ξ^{-1}$. We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate $d\to\infty$ limit of the Anderson model in $d$ spatial dimensions.

cond-mat.dis-nn↗

arXiv2018

Many-body localization transition with power-law interactions: Statistics of eigenstates

We study spectral and wavefunction statistics for many-body localization transition in systems with long-range interactions decaying as $1/r^α$ with an exponent $α$ satisfying $ d \le α\le 2d$, where $d$ is the spatial dimensionality. We refine earlier arguments and show that the system undergoes a localization transition as a function of the rescaled disorder $W^* = W / L^{2d-α} \ln L$, where $W$ is the disorder strength and $L$ the system size. This transition has much in common with that on random regular graphs. We further perform a detailed analysis of the inverse participation ratio (IPR) of many-body wavefunctions, exploring how ergodic behavior in the delocalized phase switches to fractal one at the critical point and on the localized side of the transition. Our analytical results for the scaling of the critical disorder $W$ with the system size $L$ and for the scaling of IPR in the delocalized and localized phases are supported and corroborated by exact diagonalization of spin chains.

cond-mat.dis-nn↗

arXiv2018

Superconductivity in the presence of microwaves: Full phase diagram

We address the problem of non-equilibrium superconductivity in the presence of microwave irradiation. We refine the old Eliashberg theory and generalize it to arbitrary temperatures $T$ and frequencies $ω$. Microwave radiation is shown to stimulate superconductivity in a bounded region in the $(ω,T)$ plane. In particular, for $T<0.47\, T_c$ and for $\hbarω>3.3\, k_BT_c$ superconductivity is always suppressed by a weak \emph{ac} driving. We also study the supercurrent in the presence of microwave irradiation and establish the criterion for the critical current enhancement. Our results can be qualitatively interpreted in terms of the interplay between the kinetic ("stimulation" vs. "heating") and spectral ("depairing") effects of the microwaves.

cond-mat.supr-con↗

arXiv2017

Multifractality of wave functions on a Cayley tree: From root to leaves

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site ("root") to the boundary ("leaves"). We show that the eigenfunction moments $P_q=N \left<|ψ|^{2q}(i)\right>$ exhibit a multifractal scaling $P_q\propto N^{-τ_q}$ with the volume (number of sites) $N$ at $N\to\infty$. The multifractality spectrum $τ_q$ depends on the strength of disorder and on the parameter $s$ characterizing the position of the observation point $i$ on the lattice. Specifically, $s= r/R$, where $r$ is the distance from the observation point to the root, and $R$ is the "radius" of the lattice. We demonstrate that the exponents $τ_q$ depend linearly on $s$ and determine the evolution of the spectrum with increasing disorder, from delocalized to the localized phase. Analytical results are obtained for the $n$-orbital model with $n \gg 1$ that can be mapped onto a supersymmetric $σ$ model. These results are supported by numerical simulations (exact diagonalization) of the conventional ($n=1$) Anderson tight-binding model.

cond-mat.dis-nn↗

arXiv2017

Resonant supercollisions and electron-phonon heat transfer in graphene

We study effects of strong impurities on the heat transfer in a coupled electron-phonon system in disordered graphene. A detailed analysis of the electron-phonon heat exchange assisted by such an impurity through the 'resonant supercollision' mechanism is presented. We further explore the local modification of heat transfer in a weakly disordered graphene due to a resonant scatterer and determine spatial profiles of the phonon and electron temperature around the scatterer under electrical driving. Our results are consistent with recent experimental findings on imaging resonant dissipation from individual atomic defects.

cond-mat.mes-hall↗