arXiv subjects

Doron Cohen

Publications and source records attributed to Doron Cohen.

At least 73 records · Page 4Linked to original sources

arXiv2016

Percolation, sliding, localization and relaxation in topologically closed circuits

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 the threshold for under-damped relaxation, and observe "complexity saturation" as the bias is increased.

cond-mat.stat-mech↗

arXiv2015

Chaos and two-level dynamics of the Atomtronic Quantum Interference Device

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 "systems plus bath" description in terms of Josephson-Caldeira-Leggett Hamiltonian.

cond-mat.quant-gas↗

arXiv2015

Stability and stabilization of unstable condensates

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 condensate by introducing periodic or noisy driving into the system: this is due to the Kapitza and the Zeno effects.

cond-mat.quant-gas↗

arXiv2015

Superfluidity and Chaos in low dimensional circuits

The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will randomize the velocity, as in the Drude model, and eventually the ergodic steady state will be characterized by a vanishingly small fluctuating current. However, Landau and followers have shown that this is not always the case. If elementary excitations (e.g. phonons) have higher velocity than that of the flow, simple kinematic considerations imply metastability of the vortex state: the energy of the motion cannot dissipate into phonons. On the other hand if this Landau criterion is violated the circulating current can decay. Below we show that the standard Landau and Bogoliubov superfluidity criteria fail in low-dimensional circuits. Proper determination of the superfluidity regime-diagram must account for the crucial role of chaos, an ingredient missing from the conventional stability analysis. Accordingly, we find novel types of superfluidity, associated with irregular or chaotic or breathing vortex states.

cond-mat.quant-gas↗

arXiv2015

Quantum thermalization via percolation

We highlight a dynamical anomaly in which the rate of relaxation towards thermal equilibrium in a bi-partite quantum system violates the standard linear-response (Kubo) formulation, even when the underlying dynamics is highly chaotic. This anomaly originates from an $\hbar$-dependent sparsity of the underlying quantum network of transitions. Using a minimal bi-partite Bose-Hubbard model as an example, we find that the relaxation rate acquires an anomalous $\hbar$ dependence that reflects percolation-like dynamics in energy space.

cond-mat.quant-gas↗

arXiv2014

Non-equilibrium version of the Einstein relation

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 non-trivial way on the microscopics of the sample.

cond-mat.stat-mech↗

arXiv2014

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase-space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the Peierls-Nabarro energy landscape, we deduce the various regimes in the $(Ω,u)$ parameter-space, where $u$ is the interaction, and $Ω$ is the superfluid rotation-velocity. We thus characterize the superfluid-stability and chaoticity of the many-body eigenstates throughout the Hilbert space.

cond-mat.mes-hall↗

arXiv2013

Non-equilibrium steady state and induced currents of a mesoscopically-glassy system: interplay of resistor-network theory and Sinai physics

We introduce an explicit solution for the non-equilibrium steady state (NESS) of a ring that is coupled to a thermal bath, and is driven by an external hot source with log-wide distribution of couplings. Having time scales that stretch over several decades is similar to glassy systems. Consequently there is a wide range of driving intensities where the NESS is like that of a random walker in a biased Brownian landscape. We investigate the resulting statistics of the induced current $I$. For a single ring we discuss how $sign(I)$ fluctuates as the intensity of the driving is increased, while for an ensemble of rings we highlight the fingerprints of Sinai physics on the $abs(I)$ distribution.

cond-mat.stat-mech↗

arXiv2013

Temporal fluctuations in the bosonic Josephson junction as a probe for phase space tomography

We study the long time coherence dynamics of a two-mode Bose-Hubbard model in the Josephson interaction regime, as a function of the relative phase and occupation imbalance of an arbitrary coherent preparation. We find that the variance of the long time fluctuations of the one-body coherence can be factorized as a product of the inverse participation number 1/M that depends only on the preparation, and a semi-classical function C(E) that reflects the phase space characteristics of the pertinent observable. Temporal fluctuations can thus be used as a sensitive probe for phase space tomography of quantum many-body states.

cond-mat.quant-gas↗

arXiv2013

Multiple path transport in quantum networks

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 adiabatic transport theory in the context of quantum "pumping" and "stirring". Our approach allows to address the adiabatic regime, as well as the Slow and Fast non-adiabatic regimes, on equal footing. We emphasize aspects that go beyond the familiar picture of sequential Landau-Zener crossings, taking into account Wigner-type mixing of the energy levels.

quant-ph↗

arXiv2013

Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems

We explore a minimal paradigm for thermalization, consisting of two weakly-coupled, low dimensional, non-integrable subsystems. As demonstrated for Bose-Hubbard trimers, chaotic ergodicity results in a diffusive response of each subsystem, insensitive to the details of the drive exerted on it by the other. This supports the hypothesis that thermalization can be described by a Fokker Plank equation. We also observe, however, that Levy-flight type anomalies may arise in mesoscopic systems, due to the wide range of time scales that characterize `sticky' dynamics.

cond-mat.stat-mech↗

arXiv2013

Energy absorption by "sparse" systems: beyond linear response theory

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 novel results have been obtained in the context of two prototype problems: the heating rate of particles in Billiards with vibrating walls; and the Ohmic Joule conductance of mesoscopic rings driven by electromotive force. Respectively, the obtained results are contrasted with the "Wall formula" and the "Drude formula".

quant-ph↗

arXiv2013

Coherence dynamics of kicked Bose-Hubbard dimers: Interferometric signatures of chaos

We study the coherence dynamics of a kicked two-mode Bose-Hubbard model starting with an arbitrary coherent spin preparation. For preparations in the chaotic regions of phase-space we find a generic behavior with Flouquet participation numbers that scale as the entire $N$-particle Hilbert space, leading to a rapid loss of single particle coherence. However, the chaotic behavior is not uniform throughout the chaotic sea, and unique statistics is found for preparations at the vicinity of hyperbolic points that are embedded in it. This is contrasted with the low log(N) participation that is responsible for the revivals at the vicinity of isolated hyperbolic instabilities.

cond-mat.quant-gas↗

arXiv2013

Multiple path adiabatic crossing in a 3 site ring

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.

quant-ph↗

arXiv2013

Suppression of collision-induced dephasing by periodic, erratic, or noisy driving

We compare different driving scenarios for controlling the loss of single particle coherence of an initially coherent preparation in the vicinity of the hyperbolic instability of the two-mode bose-Hubbard model. In particular we contrast the quantum Zeno suppression of decoherence by broad-band erratic or noisy driving, with the Kapitza effect obtained for high frequency periodic monochromatic driving.

cond-mat.quant-gas↗

arXiv2012

Diffusion in sparse networks: linear to semi-linear crossover

We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension it is well known that $D$ can display an abrupt percolation-like transition from diffusion ($D>0$) to sub-diffusion (D=0). A question arises whether such a transition happens in higher dimensions. Numerically $D$ can be evaluated using a resistor network calculation, or optionally it can be deduced from the spectral properties of the system. Contrary to a recent expectation that is based on a renormalization-group analysis, we deduce that $D$ is finite; suggest an "effective-range-hopping" procedure to evaluate it; and contrast the results with the linear estimate. The same approach is useful for the analysis of networks that are described by quasi-one-dimensional sparse banded matrices.

cond-mat.stat-mech↗

arXiv2012

Temporal quantum fluctuations in the fringe-visibility of atom interferometers with interacting Bose-Einstein condensate

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 employed to construct the time evolution of the initial preparation and study the temporal fluctuations of interferometric fringe visibility. The qualitative behavior and characteristic timescales of these fluctuations are set by the pertinent participation number, quantifying the spectral content of the preparation. We employ this methodology to study the Josephson-regime coherence dynamics of several initial state preparations, including a Twin-Fock state and three different coherent states that we denote as 'Zero', 'Pi', and 'Edge' (the latter two are both on-separatrix preparations, while the Zero is the standard ground sate preparation). We find a remarkable agreement between the semiclassical predictions and numerical simulations of the full quantum dynamics. Consequently, a characteristic distinct behavior is implied for each of the different preparations.

cond-mat.quant-gas↗

arXiv2012

Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality

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 behavior are necessary, neither a master equation or a classical phase-space picture are required. The simplicity and the generality of these non-equilibrium relations are demonstrated, giving very simple insights into the Physics.

cond-mat.stat-mech↗