arXiv subjects

Guy Cohen

Publications and source records attributed to Guy Cohen.

At least 37 records · Page 2Linked to original sources

arXiv2023

Empirical process sampled along a stationary process

Let $(X_{\underline{\ell}})_{\underline{\ell} \in \mathbb Z^d}$ be a real random field (r.f.) indexed by $\mathbb Z^d$ with common probability distribution function $F$. Let $(z_k)_{k=0}^\infty$ be a sequence in $\mathbb Z^d$. The empirical process obtained by sampling the random field along $(z_k)$ is $\sum_{k=0}^{n-1} [{\bf 1}_{X_{z_k} \leq s}- F(s)]$. We give conditions on $(z_k)$ implying the Glivenko-Cantelli theorem for the empirical process sampled along $(z_k)$ in different cases (independent, associated or weakly correlated random variables). We consider also the functional central limit theorem when the $X_{\underline{\ell}}$'s are i.i.d. These conditions are examined when $(z_k)$ is provided by an auxiliary stationary process in the framework of ``random ergodic theorems''.

math.PR↗

arXiv2022

Quantum Monte Carlo in the steady-state

We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.

cond-mat.str-el↗

arXiv2022

$L^2$-Quasi-compact and hyperbounded Markov operators

A Markov operator $P$ on a probability space $(S,Σ,μ)$, with $μ$ invariant, is called {\it hyperbounded} if for some $1 \le p<q \le \infty$ it maps (continuously) $L^p$ into $L^q$. We deduce from a recent result of Glück that a hyperbounded $P$ is quasi-compact, hence uniformly ergodic, in all $L^r(S,μ)$, $1<r< \infty$. We prove, using a method similar to Foguel's, that a hyperbounded Markov operator has periodic behavior similar to that of Harris recurrent operators, and for the ergodic case obtain conditions for aperiodicity. Given a probability $ν$ on the unit circle, we prove that if the convolution operator $P_νf:=ν*f$ is hyperbounded, then $ν$ is atomless. We show that there is $ν$ absolutely continuous such that $P_ν$ is not hyperbounded, and there is $ν$ with all powers singular such that $P_ν$ is hyperbounded. As an application, we prove that if $P_ν$ is hyperbounded, then for any sequence $(n_k)$ of distinct positive integers with bounded gaps, $(n_kx)$ is uniformly distributed mod 1 for $ν$ almost every $x$ (even when $ν$ is singular).

math.PR↗

arXiv2022

Reduced Dynamics of Full Counting Statistics

We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.

quant-ph↗

arXiv2022

Interaction expansion inchworm Monte Carlo solver for lattice and impurity models

Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion and explore its application to typical single- and multi-orbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. So far, for the systems studied here, it remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. The problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

cond-mat.str-el↗

arXiv2021

Dynamic graph and polynomial chaos based models for contact tracing data analysis and optimal testing prescription

In this study, we address three important challenges related to disease transmissions such as the COVID-19 pandemic, namely, (a) providing an early warning to likely exposed individuals, (b) identifying individuals who are asymptomatic, and (c) prescription of optimal testing when testing capacity is limited. First, we present a dynamic-graph based SEIR epidemiological model in order to describe the dynamics of the disease propagation. Our model considers a dynamic network that accounts for the interactions between individuals over time, such as the ones obtained by manual or automated contact tracing, and uses a diffusion-reaction mechanism to describe the state dynamics. This dynamic graph model helps identify likely exposed/infected individuals to whom we can provide early warnings, even before they display any symptoms and/or are asymptomatic. Moreover, when the testing capacity is limited compared to the population size, reliable estimation of individual's health state and disease transmissibility using epidemiological models is extremely challenging. Thus, estimation of state uncertainty is paramount for both eminent risk assessment, as well as for closing the tracing-testing loop by optimal testing prescription. Therefore, we propose the use of arbitrary Polynomial Chaos Expansion, a popular technique used for uncertainty quantification, to represent the states, and quantify the uncertainties in the dynamic model. This design enables us to assign uncertainty of the state of each individual, and consequently optimize the testing as to reduce the overall uncertainty given a constrained testing budget. These tools can also be used to optimize vaccine distribution to curb the disease spread when limited vaccines are available. We present a few simulation results that illustrate the performance of the proposed framework, and estimate the impact of incomplete contact tracing data.

q-bio.PE↗

arXiv2021

Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: "singlet weights", or projections onto particular entangled two-particle states. Using approximate theoretical arguments, we show that it is possible to construct highly specific energy- and position-resolved probes of Kondo correlations. Furthermore, we consider a quantum transport setup that can be driven away from equilibrium by a bias voltage. There, we show that singlet weights are enhanced by voltage even as the Kondo effect is weakened by it. This exposes a patently nonequilibrium mechanism for the generation of Kondo-like entanglement that is inherently different from its equilibrium counterpart.

cond-mat.mes-hall↗

arXiv2021

The Kondo Cloud in a 1D Nanowire

A recent experiment [Nature 579, 210--213 (2020)] probed the extent of the Kondo cloud in 1D by measuring the effect of electrostatic perturbations applied a distance $L$ away from the impurity on $T_K$. We study the Kondo cloud in a model proposed to describe this experimental setup, consisting of a single impurity Anderson model coupled to two semi-infinite 1D leads. In agreement with the experimental results, we find that $T_K$ is strongly affected by perturbations to the lead within the Kondo cloud. We obtain a complementary picture of the Kondo cloud in this system by observing how the Kondo state manifests itself in the local density of states of the leads, which may be observed experimentally via scanning tunneling microscopy. Our results support the existing experimental data and provide detailed predictions for future experiments seeking to characterize the Kondo cloud in this system.

cond-mat.str-el↗

arXiv2021

Heavily Doped Semiconductor Nanocrystal Quantum Dots

Doping of semiconductors by impurity atoms enabled their widespread technological application in micro and opto-electronics. For colloidal semiconductor nanocrystals, an emerging family of materials where size, composition and shape-control offer widely tunable optical and electronic properties, doping has proven elusive. This arises both from the synthetic challenge of how to introduce single impurities and from a lack of fundamental understanding of this heavily doped limit under strong quantum confinement. We develop a method to dope semiconductor nanocrystals with metal impurities providing control of the band gap and Fermi energy. A combination of optical measurements, scanning tunneling spectroscopy and theory revealed the emergence of a confined impurity band and band-tailing. Successful control of doping and its understanding provide n- and p-doped semiconductor nanocrystals which greatly enhance the potential application of such materials in solar cells, thin-film transistors, and optoelectronic devices.

cond-mat.mtrl-sci↗

arXiv2021

Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.

cond-mat.mes-hall↗

arXiv2020

Resolvent conditions and growth of powers of operators

Following Bermúdez et al. (ArXiv: 1706.03638v1), we study the rate of growth of the norms of the powers of a linear operator, under various resolvent conditions or Cesàro boundedness assumptions. We show that $T$ is power-bounded if (and only if) both $T$ and $T^*$ are absolutely Cesàro bounded. In Hilbert spaces, we prove that if $T$ satisfies the Kreiss condition, $\|T^n\|=O(n/\sqrt {\log n})$; if $T$ is absolutely Cesàro bounded, $\|T^n\|=O(n^{1/2 -\varepsilon})$ for some $\varepsilon >0$ (which depends on $T$); if $T$ is strongly Kreiss bounded, then $\|T^n\|=O((\log n)^κ)$ for some $κ>0$. We show that a Kreiss bounded operator on a reflexive space is Abel ergodic, and its Cesàro means of order $α$ converge strongly when $α>1$.

math.DS↗

arXiv2020

Correlated nonequilibrium steady states without energy flux

Floquet engineering of closed quantum systems can lead to the formation of long-lived prethermal states that, in general, eventually thermalize to infinite temperature. Coupling these driven systems to dissipative baths can stabilize such states, establishing a true nonequilibrium steady state. We demonstrate that in a certain strongly interacting lattice model coupled to a bath and driven by an electric field, such steady states can have the remarkable property that the cycle-averaged rate of energy transfer between the lattice and the baths vanishes. Despite this, we show that these states retain a clear nonequilibrium nature.

cond-mat.str-el↗

arXiv2020

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.

cond-mat.str-el↗

arXiv2020

Dynamic Control of Nonequilibrium Metal-Insulator Transitions

We demonstrate a first order metal-insulator phase transition in the repulsive, fully frustrated, single-band Hubbard model as a function of the coupling to a fermion bath. Time dependent manipulation of the bath coupling allows switching between metallic and insulating states both across the phase transition and within the coexistence region. We propose a simple nanoelectronic device for experimentally realizing dynamic control of the bath coupling. Analysis of the device characteristics shows that it can act as a two-terminal memristor.

cond-mat.str-el↗

arXiv2020

Green's function methods for single molecule junctions

We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium in general, and single molecule junctions in particular. We briefly describe experimental advances in molecular electronics, then discuss different theoretical approaches. We then focus on Green's function methods. Two characteristic energy scales governing the physics are many-body interactions within the junctions, and molecule-contact coupling. We therefore discuss weak interactions and weak coupling, as two limits that can be conveniently treated within, respectively, the standard nonequilibrium Green's function (NEGF) method and its many-body flavors (pseudoparticle and Hubbard NEGF). We argue that the intermediate regime, where the two energy scales are comparable, can in many cases be efficiently treated within the recently introduced superperturbation dual fermion approach. Finally, we review approaches for going beyond these analytically accessible limits, as embodied by recent developments in numerically exact methods based on Green's functions.

cond-mat.mes-hall↗

arXiv2020

Joint and double coboundaries of commuting contractions

Let $T$ and $S$ be commuting contractions on a Banach space $X$. The elements of $(I-T)(I-S)X$ are called {\it double coboundaries}, and the elements of $(I-T)X \cap (I-S)X$ are called {\it joint cobundaries}. For $U$ and $V$ the unitary operators induced on $L_2$ by commuting invertible measure preserving transformations which generate an aperiodic $\mathbb Z^2$-action, we show that there are joint coboundaries in $L_2$ which are not double coboundaries. We prove that if $α$,$β\in (0,1)$ are irrational, with $T_α$ and $T_β$ induced on $L_1(\mathbb T)$ by the corresponding rotations, then there are joint coboundaries in $C(\mathbb T)$ which are not measurable double cobundaries (hence not double coboundaries in $L_1(\mathbb T)$).

math.DS↗

arXiv2019

Dynamics of Kondo voltage splitting after a quantum quench

We analyze the time-dependent formation of the spectral function of an Anderson impurity model in the Kondo regime within a numerically exact real-time quantum Monte Carlo framework. At steady state, splitting of the Kondo peak occurs with nontrivial dependence on voltage and temperature, and with little effect on the location or intensity of high-energy features. Examining the transient development of the Kondo peak after a quench from an initially uncorrelated state reveals a two-stage process where the initial formation of a single central Kondo peak is followed by splitting. We analyze the time dependence of splitting in detail and demonstrate a strong dependence of its characteristic timescale on the voltage. We expect both the steady state and the transient phenomenon to be experimentally observable.

cond-mat.str-el↗

arXiv2019

On the quenched functional CLT in 2d random sceneries, examples

We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a 2d-random walk in different situations: when the r.f. is iid with a second order moment (random sceneries), or when it is generated by the action of commuting automorphisms of a torus. We consider also a quenched version of the FCLT when the random walk is replaced by a Lorentz process in the random scenery.

math.PR↗