arXiv subjects
Publications and source records attributed to Doron Cohen.
We introduce a theory for the stability of a condensate in an optical lattice. We show that the understanding of the stability-to-ergodicity transition involves the fusion of monodromy and chaos theory. Specifically, the condensate can decay if a connected chaotic pathway to depletion is formed, which requires swap of seperatrices in phase-space.
We study the many-body dynamics of stimulated Raman adiabatic passage in the presence of on-site interactions. In the classical mean-field limit, explored in Phys. Rev. Lett. {\bf 121}, 250405 (2018), interaction-induced chaos leads to the breakdown of adiabaticity under the quasi-static variation of the parameters, thus producing {\em low} sweep rate boundaries on efficient population transfer. We show that for the corresponding many-body system, alternative quantum pathways from the initial to the target state, open up at even slower sweep rates. These quantum detours avoid the chaotic classical path and hence allow a robust and efficient population transfer.
We study the process of nonlinear stimulated Raman adiabatic passage within a classical mean-fieldframework. Depending on the sign of interaction, the breakdown of adiabaticity in the interactingnonintegrable system is not related to bifurcations in the energy landscape, but rather to the emergence ofquasistochastic motion that drains the followed quasistationary state. Consequently, faster sweep rate,rather than quasistatic variation of parameters, is better for adiabaticity
Imperfections in multimode systems lead to mode-mixing and interferences between propagating modes. Such disorder is typically characterized by a finite correlation time (in quantum evolution) or correlation length (in paraxial evolution). We show that the long-scale dynamics of an initial excitation that spread in mode space can be tailored by the coherent dynamics on short-scale. In particular we unveil a universal crossover from exponential to power-law ballistic-like decay of the initial mode. Our results have applications to various wave physics frameworks, ranging from multimode fiber optics to quantum dots and quantum biology.
We propose Dual-CES -- a novel unsupervised, query-focused, multi-document extractive summarizer. Dual-CES is designed to better handle the tradeoff between saliency and focus in summarization. To this end, Dual-CES employs a two-step dual-cascade optimization approach with saliency-based pseudo-feedback distillation. Overall, Dual-CES significantly outperforms all other state-of-the-art unsupervised alternatives. Dual-CES is even shown to be able to outperform strong supervised summarizers.
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 Galilei Symmetries; Motion in magnetic field; Quantum Hall effect; Quantization of the electromagnetic field; Fock space formalism.
An active network is a prototype model in non-equilibrium statistical mechanics. It can represent, for example, a system with particles that have a self-propulsion mechanism. Each node of the network specifies a possible location of a particle, and its orientation. The orientation (which is formally like a spin degree of freedom) determines the self-propulsion direction. The bonds represent the possibility to make transitions: to hop between locations; or to switch the orientation. In systems of experimental interest (Janus particles), the self-propulsion is induced by illumination. An emergent aspect is the topological stochastic disorder (TSD). It is implied by the non-uniformity of the illumination. In technical terms the TSD reflects the local non-zero circulations (affinities) of the stochastic transitions. This type of disorder, unlike non-homogeneous magnetic field, is non-hermitian, and can lead to the emergence of a complex relaxation spectrum. It is therefore dramatically distinct from the conservative Anderson-type or Sinai-type disorder. We discuss the consequences of having TSD. In particular we illuminate 3~different routes to under-damped relaxation, and show that localization plays a major role in the analysis. Implications of the bulk-edge correspondence principle are addressed too.
We introduce a semiclassical theory for strong localization that may arise in the context of many-body thermalization. As a minimal model for thermalization we consider a few-site Bose-Hubbard model consisting of two weakly interacting subsystems that can exchange particles. The occupation of a subsystem ($x$) satisfies in the classical treatment a Fokker-Planck equation with a diffusion coefficient $D(x)$. We demonstrate that it is possible to deduce from the classical description a quantum breaktime $t^*$, and hence the manifestations of a strong localization effect. For this purpose it is essential to take the geometry of the energy shell into account, and to make a distinction between different notions of phasespace exploration.
The hallmark of superfluidity is the appearance of metastable flow-states that carry a persistent circulating current. Considering Bose-Hubbard superfluid rings, we clarify the role of "quantum chaos" in this context. We show that the standard Landau and Bogoliubov superfluidity criteria fail for such low-dimensional circuits. We also discuss the feasibility for a coherent operation of a SQUID-like setup. Finally, we address the manifestation of the strong many-body dynamical localization effect.
We consider a one-dimensional bosonic gas on a ring lattice, in the presence of a localized barrier, and under the effect of an artificial gauge field. By means of exact diagonalization we study the persistent currents at varying interactions and barrier strength, for various values of lattice filling. While generically the persistent currents are strongly suppressed in the Mott insulator phase, they show a resonant behaviour when the barrier strength becomes of the order of the interaction energy. We explain this phenomenon using an effective single-particle model. We show that this effect is robust at finite temperature, up the temperature scale where persistent currents vanish.
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 simply $D_r = (1/8)w^2/D$, but has a non-monotonic dependence on $w/D$. Furthermore, the calculation of the radial moments is dominated by the far non-Gaussian tails of the $\log(r)$ distribution.
The session search task aims at best serving the user's information need given her previous search behavior during the session. We propose an extended relevance model that captures the user's dynamic information need in the session. Our relevance modelling approach is directly driven by the user's query reformulation (change) decisions and the estimate of how much the user's search behavior affects such decisions. Overall, we demonstrate that, the proposed approach significantly boosts session search performance.
A semiclassical theory is provided for the metastability regime-diagram of atomtronic superfluid circuits. Such circuits typically exhibit high-dimensional chaos; and non-linear resonances that couple the Bogoliubov excitations manifest themselves. Contrary to the expectation these resonances do not originate from the familiar Beliaev and Landau damping terms. Rather, they are described by a variant of the Cherry Hamiltonian of celestial mechanics. Consequently we study the induced decay process, and its dependence on the number of sites and of condensed particles.
We consider thermal transport in low-dimensional disordered harmonic networks of coupled masses. Utilizing known results regarding Anderson localization, we derive the actual dependence of the thermal conductance $G$ on the length $L$ of the sample. This is required by nanotechnology implementations because for such networks Fourier's law $G \propto 1/L^α$ with $α=1$ is violated. In particular we consider "glassy" disorder in the coupling constants, and find an anomaly which is related by duality to the Lifshitz-tail regime in the standard Anderson model.
The relaxation process of a diffusive ring becomes under-damped if the bias (so called affinity) exceeds a critical threshold value, aka delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak-link into the circuit, and illuminate some subtleties that arise while taking the continuum limit of the discrete model.
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 integral exponent. While the zeroth-order expansion results in a remarkably simple, yet nontrivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called "dephasing representation", circumventing the use of semiclassical propagator as in the original derivation. We also obtain approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact.
Quantum localization within an energy-shell of a closed quantum system stands in contrast to the ergodic assumption of Boltzmann, and to the corresponding eigenstate thermalization hypothesis. The familiar case is the real-space "Anderson localization" and its many-body Fock-space version. We use the term "Hilbert-space localization" in order to emphasize the more general phase-space context. Specifically, we introduce a unifying picture that extends the semiclassical perspective of Heller, which relates the localization measure to the probability of return. We illustrate our approach by considering several systems of experimental interest, referring in particular to the Bosonic Josephson tunneling junction. We explore the dependence of the localization measure on the initial state, and on the strength of the many-body interactions using a novel recursive projection method.
Linear response theory relates the response of a system to the power-spectrum of its fluctuations. However, the response to external driving in realistic models exhibits a pronounced non-linear blurring of the spectral line-shape. Considering a driven Bose-Hubbard trimer model we figure out what is the hidden time scale that controls this smearing effect. Contrary to conventional wisdom, the Fermi-golden-rule picture fails miserably in predicting the non-linear width of the transitions. Instead, if the system has a classical limit, the determination of the hidden time scale requires taking into account the underlying classical phase-space dynamics.