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Sep 19, 2013
09/13

by
Doron Cohen

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There are three regimes in the theory of energy absorption: The adiabatic regime, the linear-response (Kubo) regime, and the non-perturbative regime. The mesoscopic Drude formula for electrical conductance, and the wall formula for friction, can be regarded as special cases of the general formulation of the dissipation problem. The overview is based on a research report for 1998-2000.

Source: http://arxiv.org/abs/cond-mat/0010367v1

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Sep 22, 2013
09/13

by
Doron Cohen

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We try to clarify what are the genuine quantal effects that are associated with generalized Brownian Motion (BM). All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution of the classical Langevin equation. Non-stochastic, genuine quantum mechanical effects, are found for a model that takes into account either the disordered or the chaotic nature of some environment.

Source: http://arxiv.org/abs/chao-dyn/9704016v1

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Sep 22, 2013
09/13

by
Doron Cohen

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The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in the field of `Quantum Chaos'. Starting from the semiclassical trace formula, we formulate a quantal-classical duality relation that connects the spectral properties of the quantal spectrum to the statistical properties of lengths of periodic orbits. By...

Source: http://arxiv.org/abs/chao-dyn/9612014v3

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Jul 20, 2013
07/13

by
Doron Cohen

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These are the lecture notes for quantum and statistical mechanics courses that are given by DC at Ben-Gurion University. They are complementary to "Lecture Notes in Quantum Mechanics" [arXiv: quant-ph/0605180]. Some additional topics are covered, including: introduction to master equations; non-equilibrium processes; fluctuation theorems; linear response theory; adiabatic transport; the Kubo formalism; and the scattering approach to mesoscopics.

Source: http://arxiv.org/abs/1107.0568v2

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Sep 23, 2013
09/13

by
Doron Cohen

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Current can be pumped through a closed system by changing parameters (or fields) in time. Linear response theory (the Kubo formula) allows to analyze both the charge transport and the associated dissipation effect. We make a distinction between adiabatic and non-adiabatic regimes, and explain the subtle limit of an infinite system. As an example we discuss the following question: What is the amount of charge which is pushed by a moving scatterer? In the low frequency (DC) limit we can write...

Source: http://arxiv.org/abs/cond-mat/0510318v1

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Aug 30, 2021
08/21

by
Doron Cohen

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Pre-registration of a new experiement

Source: https://osf.io/4haqe/

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Sep 22, 2013
09/13

by
Doron Cohen

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We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an equivalent Master equation. Unlike the case of the Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest themselves due to the disordered nature of the environment. Using Wigner picture of the dynamics we distinguish between two...

Source: http://arxiv.org/abs/cond-mat/9805023v2

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Jul 20, 2013
07/13

by
Doron Cohen

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We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic physics can be regarded as two special results of the general formulation. We assume a time-dependent Hamiltonian $H(Q,P;x(t))$ with $x(t)=Vt$, where $V$ is slow in a classical sense. The rate-of-change $V$ is not necessarily slow in the quantum-mechanical sense....

Source: http://arxiv.org/abs/cond-mat/9902168v3

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Sep 18, 2013
09/13

by
Doron Cohen

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Consider a multichannel closed ring with disorder. In the semiclassical treatment its conductance is given by the Drude formula. Quantum mechanics challenge this result both in the limit of strong disorder (eigenstates are not quantum-ergodic in real space) and in the limit of weak disorder (eigenstates are not quantum-ergodic in momentum space). Consequently the analysis of conductance requires going beyond linear response theory, leading to a resistor network picture of transitions between...

Source: http://arxiv.org/abs/cond-mat/0611663v3

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Sep 18, 2013
09/13

by
Doron Cohen

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These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory; Entanglement; Quantum computation; Wigner-Weyl formalism; The adiabatic picture; Berry phase; Linear response theory; Kubo formula; Modern approach to scattering theory with mesoscopic orientation; Theory of the resolvent and the Green function; Gauge and...

Source: http://arxiv.org/abs/quant-ph/0605180v5

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Sep 11, 2021
09/21

by
Doron Cohen

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Source: https://osf.io/5hwzj/

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Sep 19, 2013
09/13

by
Doron Cohen

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Current can be pumped through a closed system by changing parameters (or fields) in time. The Kubo formula allows to distinguish between dissipative and non-dissipative contributions to the current. We obtain a Green function expression and an $S$ matrix formula for the associated terms in the generalized conductance matrix: the "geometric magnetism" term that corresponds to adiabatic transport; and the "Fermi golden rule" term which is responsible to the irreversible...

Source: http://arxiv.org/abs/cond-mat/0304678v4

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Sep 22, 2013
09/13

by
Doron Cohen

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The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is $\Delta_b\propto\hbar$, which is known as the non-universal energy scale, or as the bandwidth, or as the Thouless energy. Associated with these two energy scales are two special quantum-mechanical (QM) regimes in the theory of driven system. These...

Source: http://arxiv.org/abs/quant-ph/0201088v1

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Sep 22, 2013
09/13

by
Doron Cohen

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Quantum pumping in closed systems is considered. We explain that the Kubo formula contains all the physically relevant ingredients for the calculation of the pumped charge ($Q$) within the framework of linear response theory. The relation to the common formulations of adiabatic transport and ``geometric magnetism" is clarified. We distinguish between adiabatic and dissipative contributions to $Q$. On the one hand we observe that adiabatic pumping does not have to be quantized. On the other...

Source: http://arxiv.org/abs/cond-mat/0307619v2

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Sep 23, 2013
09/13

by
Doron Cohen

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Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and try to relate it to the problem of quantal particle that interacts with an effective harmonic bath.

Source: http://arxiv.org/abs/chao-dyn/9909024v2

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Sep 18, 2013
09/13

by
Doron Cohen

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The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.

Source: http://arxiv.org/abs/0704.1087v1

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Sep 19, 2013
09/13

by
Doron Cohen

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The motion of a particle under the influence of a dynamical disorder is described by the DLD model. One motivation is to understand the motion of an electron inside a metal; Another is to understand quantal Brownian motion. The overview is based on a research report for 1996-1998.

Source: http://arxiv.org/abs/cond-mat/0010366v1

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Sep 24, 2013
09/13

by
Doron Cohen

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We consider the motion of a particle, taking into account its interaction with environmental degrees of freedom. The dephasing time is determined by the nature of the environment, and depends on the particle velocity. Our interest is in the case where the environment consists of few chaotic degrees of freedom. We obtain results for the dephasing time, and compare them with those of the effective-bath approach. The latter approach is based on the conjecture that the environment can be modelled...

Source: http://arxiv.org/abs/cond-mat/0103279v2

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Sep 22, 2013
09/13

by
Doron Cohen

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Driven chaotic systems are of interest in mesoscopic physics, as well as in nuclear, atomic and molecular physics. Such systems [coordinates $(Q,P)$]$ tend to absorb energy. This irreversible effect is known as dissipation. "Driving" means that a parameter $x$ is changed in time. More generally, $x$ may be a dynamical variable. In such case the interaction of $(x,p)$ with the environmental degrees of freedom $(Q,P)$ leads to dephasing as well as to dissipation. We introduce a general...

Source: http://arxiv.org/abs/quant-ph/0403061v2

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Sep 19, 2013
09/13

by
Doron Cohen

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Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the...

Source: http://arxiv.org/abs/cond-mat/0208233v4

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48

Sep 23, 2013
09/13

by
Doron Cohen

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The analysis of the response to driving in the case of weakly chaotic or weakly interacting systems should go beyond linear response theory. Due to the "sparsity" of the perturbation matrix, a resistor network picture of transitions between energy levels is essential. The Kubo formula is modified, replacing the "algebraic" average over the squared matrix elements by a "resistor network" average. Consequently the response becomes semi-linear rather than linear. Some...

Source: http://arxiv.org/abs/1202.5871v3

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Sep 23, 2013
09/13

by
Doron Cohen

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The angle coordinate of the Quantum Kicked Rotator problem is treated as if it were an extended coordinate. A new mechanism for destruction of coherence by noise is analyzed using both heuristic and formal approach. Its effectiveness constitutes a manifestation of long-range non-trivial dynamical correlations. Perturbation theory fails to quantify certain aspects of this effect. In the perturbative case, for sufficiently weak noise, the diffusion coefficient ${\cal D}$ is just proportional to...

Source: http://arxiv.org/abs/chao-dyn/9909016v1

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Sep 20, 2013
09/13

by
Doron Cohen

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A new model that generalizes the study of quantum Brownian motion (BM) is constructed. We consider disordered environment that may be either static (quenched), noisy or dynamical. The Zwanzig-Caldeira-Leggett BM-model constitutes formally a special case where the disorder auto-correlation length is taken to be infinite. Alternatively, localization problem is obtained if the noise auto-correlation time is taken to be infinite. Also the general case of weak nonlinear coupling to thermal, possibly...

Source: http://arxiv.org/abs/chao-dyn/9611013v3

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Sep 20, 2013
09/13

by
Doron Cohen

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Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is...

Source: http://arxiv.org/abs/cond-mat/9810395v3

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6.0

Jun 28, 2018
06/18

by
Doron Cohen

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It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but what about a condensation in an excited mode? We discuss some results that have been obtained for a 2-mode bosonic Josephson junction, and for a 3-mode minimal-model of a superfluid circuit. Additionally we mention the possibility to stabilize an unstable...

Topics: Quantum Physics, Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1510.02279

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4.0

Jun 28, 2018
06/18

by
Jiri Vanicek; Doron Cohen

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The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1510.03140

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48

Sep 22, 2013
09/13

by
Tsampikos Kottos; Doron Cohen

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The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving reversal". In the latter context the time of maximum return (compensation) should substitute the inappropriate notion of "echo" time. Non-perturbative features manifest themselves in the energy spreading process. This is...

Source: http://arxiv.org/abs/cond-mat/0201148v3

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55

Sep 22, 2013
09/13

by
Doron Cohen; Tsampikos Kottos

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Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega| \omega_{cl}$, and the shape of the response function becomes $A$ dependent.

Source: http://arxiv.org/abs/cond-mat/0004022v2

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44

Sep 18, 2013
09/13

by
Tsampikos Kottos; Doron Cohen

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Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a random-matrix theory (RMT) approach. RMT can be trusted only to the extend that it gives trivial results that are implied by first-order perturbation theory. Non-perturbative effects are sensitive to the underlying classical...

Source: http://arxiv.org/abs/cond-mat/0105274v1

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Sep 18, 2013
09/13

by
Doron Cohen; Yoav Etzioni

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The multimode conductance of a {\em closed} ring is found within the framework of a scattering approach. The expression can be regarded as a generalization of the Landauer formula. The treatment is essentially {\em classical} because we assume short coherence time. Our starting point is the Kubo formalism, but we also use a master equation approach for the derivation. As an example we calculate the conductance of a multimode waveguide with an attached cavity.

Source: http://arxiv.org/abs/cond-mat/0504756v2

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4.0

Jun 30, 2018
06/18

by
Daniel Hurowitz; Doron Cohen

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The celebrated Einstein relation between the diffusion coefficient $D$ and the drift velocity $v$ is violated in non-equilibrium circumstances. We analyze how this violation emerges for the simplest example of a Brownian motion on a lattice, taking into account the interplay between the periodicity, the randomness and the asymmetry of the transition rates. Based on the non-equilibrium fluctuation theorem the $v/D$ ratio is found to be a non-linear function of the affinity. Hence it depends in a...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1404.7681

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Sep 22, 2013
09/13

by
Doron Cohen; Tsampikos Kottos

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Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing $\Delta$, and the bandwidth $\Delta_b\propto\hbar$. This implies that with respect to driving such systems have an adiabatic, a perturbative, and a non-perturbative regimes. A "strong" quantal non-perturbative response effect is found for {\em disordered} systems that are described by random matrix theory models. Is there a similar effect for quantized {\em chaotic} systems?...

Source: http://arxiv.org/abs/cond-mat/0205017v2

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Sep 19, 2013
09/13

by
Maya Chuchem; Doron Cohen

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The conventional probabilistic point of view implies that if a particle has a probability $p$ to make a transition from one site to another site, then the average transport should be $ =p}$ with a variance $Var(Q)=(1-p)p$. In the quantum mechanical context this observation becomes a non-trivial manifestation of restricted quantum-classical correspondence. We demonstrate this observation by considering the full counting statistics which is associated with a two level coherent transition in the...

Source: http://arxiv.org/abs/0708.4237v3

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Sep 22, 2013
09/13

by
Doron Cohen; Yoseph Imry

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We discuss the significance and the calculation of dephasing at low temperatures. The particle is moving diffusively due to a static disorder configuration, while the interference between classical paths is suppressed due to the interaction with a dynamical environment. At high temperatures we may use the `white noise approximation' (WNA), while at low temperatures we distinguish the contribution of `zero point fluctuations' (ZPF) from the `thermal noise contribution' (TNC). We study the...

Source: http://arxiv.org/abs/cond-mat/9807038v2

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Sep 22, 2013
09/13

by
Geva Arwas; Doron Cohen

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We find an exact expression for the current ($I$) that flows via a tagged bond from a site ("dot") whose potential ($u$) is varied in time. We show that the analysis reduces to that of calculating time dependent probabilities, as in the stochastic formulation, but with splitting (branching) ratios that are not bounded within $[0,1]$. Accordingly our result can be regarded as a multiple-path version of the continuity equation. It generalizes results that have been obtained from...

Source: http://arxiv.org/abs/1210.7051v2

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Sep 19, 2013
09/13

by
Doron Cohen; Baruch Horovitz

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The motion of a particle in a ring of length L is influenced by a dirty metal environment whose fluctuations are characterized by a short correlation distance $\ell < < L$. We analyze the induced decoherence process, and compare the results with those obtained in the opposing Caldeira-Leggett limit ($\ell >> L$). A proper definition of the dephasing factor that does not depend on a vague semiclassical picture is employed. Some recent Monte-Carlo results about the effect of finite...

Source: http://arxiv.org/abs/0708.0965v2

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Sep 18, 2013
09/13

by
Doron Cohen; Baruch Horovitz

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We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass...

Source: http://arxiv.org/abs/0707.1993v2

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Sep 23, 2013
09/13

by
Doron Cohen; Yoseph Imry

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We obtain the Crooks and the Jarzynski non-equilibrium fluctuation relations using a direct quantum-mechanical approach for a finite system that is either isolated or coupled not too strongly to a heat bath. These results were hitherto derived mostly in the classical limit. The two main ingredients in the picture are the time-reversal symmetry and the application of the first law to the case where an agent performs work on the system. No further assumptions regarding stochastic or Markovian...

Source: http://arxiv.org/abs/1202.4529v3

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Sep 23, 2013
09/13

by
Swarnali Bandopadhyay; Doron Cohen

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We study the role of zero-point-fluctuations (ZPF) in dephasing at low temperature. Unlike the Caldeira-Leggett model where the interaction is with an homogeneous fluctuating field of force, here we consider the effect of short range scattering by localized bath modes. We find that in presence of ZPF the inelastic cross-section gets renormalized. Thus indirectly ZPF might contribute to the dephasing at low temperature.

Source: http://arxiv.org/abs/0801.1202v2

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Sep 17, 2013
09/13

by
Maya Chuchem; Doron Cohen

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A current can be induced in a closed device by changing control parameters. The amount $Q$ of particles that are transported via a path of motion, is characterized by its expectation value $ $, and by its variance $Var(Q)$. We show that quantum mechanics invalidates some common conceptions about this statistics. We first consider the process of a double path crossing, which is the prototype example for counting statistics in multiple path non-trivial geometry. We find out that contrary to the...

Source: http://arxiv.org/abs/0912.1690v1

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Jul 20, 2013
07/13

by
Daniel Hurowitz; Doron Cohen

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A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a bath. In the stochastic case there is an analogy to the physics of percolating glassy systems, and an extension of the fluctuation-dissipation phenomenology is proposed. In the mesoscopic case the quantum NESS might differ enormously from the...

Source: http://arxiv.org/abs/1007.0766v3

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Sep 18, 2013
09/13

by
Maya Chuchem; Doron Cohen

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The amount $Q$ of particles that are transported via a path of motion is characterized by its expectation value $ $ and by its variance $Var(Q)$. We analyze what happens if a particle has two optional paths available to get from one site to another site, and in particular what is $Var(Q)$ for the current which is induced in a quantum stirring device. It turns out that coherent splitting and the stirring effect are intimately related and cannot be understood within the framework of the...

Source: http://arxiv.org/abs/0704.3506v4

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Sep 20, 2013
09/13

by
Itamar Sela; Doron Cohen

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A circulating current can be induced in the Fermi sea by displacing a scatterer, or more generally by integrating a quantum pump into a closed circuit. The induced current may have either the same or the opposite sense with respect to the "pushing" direction of the pump. We work out explicit expressions for the associated geometric conductance using the Kubo-Dirac monopoles picture, and illuminate the connection with the theory of adiabatic passage in multiple path geometry.

Source: http://arxiv.org/abs/0802.2364v2

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Sep 19, 2013
09/13

by
Jiri Vanicek; Doron Cohen

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For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes, and to the observation that semiclassical tools are useful in the latter case. We discuss what is "left" from this theory in the case of one-dimensional systems. We demonstrate that the remarkably accurate {\em uniform}...

Source: http://arxiv.org/abs/quant-ph/0303103v2

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Jul 22, 2013
07/13

by
Itamar Sela; Doron Cohen

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The simplest one-dimensional model for the studying of non-trivial geometrical effects is a ring shaped device which is formed by joining two arms. We explore the possibility to model such a system as a two level system (TLS). Of particular interest is the analysis of quantum stirring, where it is not evident that the topology is properly reflected within the framework of the TLS modeling. On the technical side we provide a practical "neighboring level" approximation for the analysis...

Source: http://arxiv.org/abs/0807.2572v2

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6.0

Jun 28, 2018
06/18

by
Geva Arwas; Doron Cohen

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We study the Atomtronics Quantum Interference Device employing a semiclassical perspective. We consider an $M$ site ring that is described by the Bose-Hubbard Hamiltonian. Coherent Rabi oscillations in the flow of the current are feasible, with an enhanced frequency due to to chaos-assisted tunneling. We highlight the consequences of introducing a weak-link into the circuit. In the latter context we clarify the phase-space considerations that are involved in setting up an effective...

Topics: Quantum Physics, Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1510.04438

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3.0

Jun 28, 2018
06/18

by
Daniel Hurowitz; Doron Cohen

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Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization" of eigenstates of non-hermitian Hamiltonians has been addressed by Hatano, Nelson, and followers. But we show that for a conservative stochastic process the implied spectral properties are dramatically different. In particular we determine...

Topics: Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1512.00258

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3.0

Jun 30, 2018
06/18

by
Dekel Shapira; Doron Cohen

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We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate~$w$, and the angular diffusion coefficient~$D$. We carry out an exact analysis to determine the drift and the diffusion coefficient of $\log(r)$, where $r$ is the radial coordinate. The results go beyond the heuristic lognormal description that is implied by the central limit theorem. Contrary to the common "Quantum Zeno" approximation, the radial diffusion is not...

Topics: Quantum Gases, Statistical Mechanics, Condensed Matter

Source: http://arxiv.org/abs/1701.01381

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Sep 18, 2013
09/13

by
Dotan Davidovich; Doron Cohen

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We find an exact expression for the current that is induced in a 3 site ring during a multiple-path adiabatic crossing. The understanding of the dynamics requires to go beyond the two-level phenomenology. In particular we highlight a prototype process, "adiabatic metamorphosis", during which current is flowing through a non-accessible site. This helps to understand the crossover from coherent non-classical splitting to stochastic noisy-alike partitioning of the current.

Source: http://arxiv.org/abs/1211.0766v2

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Sep 23, 2013
09/13

by
Doron Cohen; Amichay Vardi

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We formulate a semiclassical approach to study the dynamics of coherence loss and revival in a Bose-Josephson dimer. The phase-space structure of the bi-modal system in the Rabi, Josephson, and Fock interaction regimes, is reviewed and the prescription for its WKB quantization is specified. The local density of states (LDOS) is then deduced for any given preparation from its semiclassical projection onto the WKB eigenstates. The LDOS and the non-linear variation of its level-spacing are...

Source: http://arxiv.org/abs/1110.1956v2