arXiv subjects

Roland Ketzmerick

Publications and source records attributed to Roland Ketzmerick.

At least 55 records · Page 3Linked to original sources

arXiv2013

Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems

Bose-Einstein condensation, the macroscopic occupation of a single quantum state, appears in equilibrium quantum statistical mechanics and persists also in the hydrodynamic regime close to equilibrium. Here we show that even when a degenerate Bose gas is driven into a steady state far from equilibrium, where the notion of a single-particle ground state becomes meaningless, Bose-Einstein condensation survives in a generalized form: the unambiguous selection of an odd number of states acquiring large occupations. Within mean-field theory we derive a criterion for when a single and when multiple states are Bose selected in a non-interacting gas. We study the effect in several driven-dissipative model systems, and propose a quantum switch for heat conductivity based on shifting between one and three selected states.

cond-mat.stat-mech↗

arXiv2013

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.

nlin.CD↗

arXiv2012

Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea

Generic 2D Hamiltonian systems possess partial barriers in their chaotic phase space that restrict classical transport. Quantum mechanically the transport is suppressed if Planck's constant h is large compared to the classical flux, h >> Phi, such that wave packets and states are localized. In contrast, classical transport is mimicked for h << Phi. Designing a quantum map with an isolated partial barrier of controllable flux Phi is the key to investigating the transition from this form of quantum localization to mimicking classical transport. It is observed that quantum transport follows a universal transition curve as a function of the expected scaling parameter Phi/h. We find this curve to be symmetric to Phi/h=1, having a width of two orders of magnitude in Phi/h, and exhibiting no quantized steps. We establish the relevance of local coupling, improving on previous random matrix models relying on global coupling. It turns out that a phenomenological 2x2-model gives an accurate analytical description of the transition curve.

nlin.CD↗

arXiv2012

Complex paths for regular-to-chaotic tunneling rates

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical approach based on complex paths for the prediction of dynamical tunneling rates from regular tori to the chaotic region. This approach is demonstrated for the standard map giving excellent agreement with numerically determined tunneling rates.

nlin.CD↗

arXiv2012

Coupling of bouncing-ball modes to the chaotic sea and their counting function

We study the coupling of bouncing-ball modes to chaotic modes in two-dimensional billiards with two parallel boundary segments. Analytically, we predict the corresponding decay rates using the fictitious integrable system approach. Agreement with numerically determined rates is found for the stadium and the cosine billiard. We use this result to predict the asymptotic behavior of the counting function N_bb(E) ~ E^δ. For the stadium billiard we find agreement with the previous result δ= 3/4. For the cosine billiard we derive δ= 5/8, which is confirmed numerically and is well below the previously predicted upper bound δ=9/10.

nlin.CD↗

arXiv2011

Partial Weyl Law for Billiards

For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $Γ$ of phase space. The leading term is proportional to the area of the billiard times the phase-space fraction of $Γ$. The boundary term is proportional to the fraction of the boundary where parallel trajectories belong to $Γ$. Our result is numerically confirmed for the mushroom billiard and the generic cosine billiard, where we count the number of chaotic and regular states, and for the elliptical billiard, where we consider rotating and oscillating states.

quant-ph↗

arXiv2011

Direct Regular-to-Chaotic Tunneling Rates Using the Fictitious Integrable System Approach

In systems with a mixed phase space, where regular and chaotic motion coexists, regular states are coupled to the chaotic region by dynamical tunneling. We give an overview on the determination of direct regular-to-chaotic tunneling rates using the fictitious integrable system approach. This approach is applied to different kicked systems, including the standard map, and successfully compared with numerical data. This text corresponds to Chapter 6 of the book: Dynamical Tunneling - Theory and Experiment, edited by S. Keshavamurthy and P. Schlagheck [Taylor and Francis CRC (2011)]. For a more extensive exposition see [Phys. Rev. E 82, 056208 (2010); arXiv:1009.0418v2].

nlin.CD↗

arXiv2011

Fractional-Power-Law Level-Statistics due to Dynamical Tunneling

For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power law of the level-spacing distribution P(s) over a wide range of small spacings s. Going beyond Berry-Robnik statistics, we take into account that dynamical tunneling rates between the regular and the chaotic region vary over many orders of magnitude. This results in a prediction of P(s) which excellently describes the spectral data of the standard map. Moreover, we show that the power-law exponent is proportional to the effective Planck constant h.

nlin.CD↗

arXiv2010

Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach

We review the fictitious integrable system approach which predicts dynamical tunneling rates from regular states to the chaotic region in systems with a mixed phase space. It is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the regular island. We focus on the direct regular-to-chaotic tunneling process which dominates, if nonlinear resonances within the regular island are not relevant. For quantum maps, billiard systems, and optical microcavities we find excellent agreement with numerical rates for all regular states.

nlin.CD↗

arXiv2010

Statistical mechanics of Floquet systems with regular and chaotic states

We investigate the asymptotic state of time-periodic quantum systems with regular and chaotic Floquet states weakly coupled to a heat bath. The asymptotic occupation probabilities of these two types of states follow fundamentally different distributions. Among regular states the probability decreases from the state in the center of a regular island to the outermost state by orders of magnitude, while chaotic states have almost equal probabilities. We derive an analytical expression for the occupations of regular states of kicked systems, which depends on the winding numbers of the regular tori and the parameters temperature and driving frequency. For a constant winding number within a regular island it simplifies to Boltzmann-like weights $\exp(-\betaeff \Ereg_m)$, similar to time-independent systems. For this we introduce the regular energies $\Ereg_m$ of the quantizing tori and an effective winding-number-dependent temperature $1/\betaeff$, different from the actual bath temperature. Furthermore, the occupations of other typical Floquet states in a mixed phase space are studied, i.e. regular states on nonlinear resonances, beach states, and hierarchical states, giving rise to distinct features in the occupation distribution. Avoided crossings involving a regular state lead to drastic consequences for the entire set of occupations. We introduce a simplified rate model whose analytical solutions describe the occupations quite accurately.

cond-mat.stat-mech↗

arXiv2010

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given $\hbar$-regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

nlin.CD↗

arXiv2009

Switching mechanism in periodically driven quantum systems with dissipation

We introduce a switching mechanism in the asymptotic occupations of quantum states induced by the combined effects of a periodic driving and a weak coupling to a heat bath. It exploits one of the ubiquitous avoided crossings in driven systems and works even if both involved Floquet states have small occupations. It is independent of the initial state and the duration of the driving. As a specific example of this general switching mechanism we show how an asymmetric double well potential can be switched between the lower and the upper well by a periodic driving that is much weaker than the asymmetry.

cond-mat.stat-mech↗

arXiv2009

Quality factors and dynamical tunneling in annular microcavities

The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell's equations.

physics.optics↗

arXiv2008

Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies

The statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath exhibits some radical differences from the traditional statistical mechanics of undriven systems. In Floquet systems all quasienergies can be placed in a finite frequency interval, and the number of near degeneracies in this interval grows without limit as the dimension N of the Hilbert space increases. This leads to pathologies, including drastic changes in the Floquet states, as N increases. In earlier work these difficulties were put aside by fixing N, while taking the coupling to the bath to be smaller than any quasienergy difference. This led to a simple explicit theory for the reduced density matrix, but with some major differences from the usual time independent statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated Hilbert space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual neglect of bath memory effects within the Born and Markov approximations. As we seek higher accuracy by increasing N, we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive the steady state reduced density matrix without restriction on the size of quasienergy splittings. In general, it is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where quasienergy near degeneracies routinely appear. The explicit form of our results for the denisty matrix gives a consistent prescription for the statistical mechanics for many periodically driven systems with N infinite, in spite of the Floquet state pathologies.

cond-mat.stat-mech↗

arXiv2008

On universality of algebraic decays in Hamiltonian systems

Hamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent.

nlin.CD↗

arXiv2007

Universality in the flooding of regular islands by chaotic states

We investigate the structure of eigenstates in systems with a mixed phase space in terms of their projection onto individual regular tori. Depending on dynamical tunneling rates and the Heisenberg time, regular states disappear and chaotic states flood the regular tori. For a quantitative understanding we introduce a random matrix model. The resulting statistical properties of eigenstates as a function of an effective coupling strength are in very good agreement with numerical results for a kicked system. We discuss the implications of these results for the applicability of the semiclassical eigenfunction hypothesis.

nlin.CD↗

arXiv2004

Directed Chaotic Transport in Hamiltonian Ratchets

We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport, like a mixed classical phase space, and elucidate a sum rule that relates the contributions of different phase-space components to transport with each other. We show that regular ratchet transport can be directed against an external potential gradient while chaotic ballistic transport is restricted to unbiased systems. For quantized Hamiltonian ratchets we study transport in terms of the evolution of wave packets and derive a semiclassical expression for the distribution of level velocities which encode the quantum transport in the Floquet band spectra. We discuss the role of dynamical tunneling between transporting islands and the chaotic sea and the breakdown of transport in quantum ratchets with broken spatial periodicity.

nlin.CD↗

arXiv2004

Electrons in 2D periodic magnetic and electric fields: Avoided band crossings, metal-insulator transitions, and changes in the spreading direction

We study the energy spectrum and wave packet dynamics of electrons in a two-dimensional periodic potential subject to a perpendicular spatially modulated magnetic field. We observe avoided band crossings, metal-insulator transitions, and changes in the spreading direction of wave packets in two new situations: (i) for a purely magnetic modulation and (ii) in the limit of weak electric and magnetic modulations, where the Landau band coupling can be neglected. In the second case the corresponding classical system is no longer chaotic but integrable, whereby these phenomena are not expected. We argue that they are due to tunneling.

cond-mat.mes-hall↗