arXiv subjects

Peter Reimann

Publications and source records attributed to Peter Reimann.

At least 37 records · Page 2Linked to original sources

arXiv2020

Temporal relaxation of gapped many-body quantum systems

Typicality of the orthogonal dynamics (TOD) is established as a generic feature of temporal relaxation processes in isolated many-body quantum systems. The basic idea in the simplest case is that the transient non-equilibrium behavior is mainly governed by the component of the time-evolved system state parallel to the initial state, while the orthogonal component appears as equilibrated right from the beginning. The main emphasis is laid on the largely unexplored and particularly challenging case that one energy level exhibits a much larger population than all the others. Important examples are gapped many-body systems at low energies, for instance due to a quantum quench. A general analytical prediction is derived and is found to compare very well with various numerically exact results.

cond-mat.stat-mech↗

arXiv2019

Transportless equilibration in isolated many-body quantum systems

A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature.

cond-mat.stat-mech↗

arXiv2019

Typicality of Prethermalization

Prethermalization refers to the remarkable relaxation behavior which an integrable many-body system in the presence of a weak integrability-breaking perturbation may exhibit: After initial transients have died out, it stays for a long time close to some non-thermal steady state, but on even much larger time scales it ultimately switches over to the proper thermal equilibrium behavior. By extending Deutsch's conceptual framework from Phys. Rev. A 43, 2046 (1991), we analytically predict that prethermalization is a typical feature for a very general class of such weakly perturbed systems.

cond-mat.stat-mech↗

arXiv2019

Full expectation value statistics for randomly sampled pure states in high-dimensional quantum systems

We explore how the expectation values $\langleψ|A| ψ\rangle$ of a largely arbitrary observable $A$ are distributed when normalized vectors $|ψ\rangle$ are randomly sampled from a high dimensional Hilbert space. Our analytical results predict that the distribution exhibits a very narrow peak of approximately Gaussian shape, while the tails significantly deviate from a Gaussian behavior. In the important special case that the eigenvalues of $A$ satisfy Wigner's semicircle law, the expectation value distribution for asymptotically large dimensions is explicitly obtained in terms of a large deviation function, which exhibits two symmetric non-analyticities akin to critical points in thermodynamics.

cond-mat.stat-mech↗

arXiv2018

Dynamical typicality of isolated many-body quantum systems

Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable $A$, are very likely to exhibit also very similar expectation values when evolving in time according to the pertinent Schrödinger equation. We unify and generalize a variety of previous findings of this type for sufficiently high dimensional quantum mechanical model systems. Particular emphasize is put on the necessary and sufficient conditions, which the initial expectation value and the spectrum of $A$ have to fulfill.

cond-mat.stat-mech↗

arXiv2018

Dynamical typicality approach to eigenstate thermalization

We consider the set of all initial states within a microcanonical energy shell of an isolated many-body quantum system, which exhibit the same, arbitrary but fixed non-equilibrium expectation value for some given observable $A$. On condition that this set is not too small, it is shown by means of a dynamical typicality approach that most such initial states exhibit thermalization if and only if $A$ satisfies the so-called weak eigenstate thermalization hypothesis (wETH). Here, thermalization means that the expectation value of $A$ spends most of its time close to the microcanonical value after initial transients have died out. The wETH means that, within the energy shell, most eigenstates of the pertinent system Hamiltonian exhibit very similar expectation values of $A$.

cond-mat.stat-mech↗

arXiv2017

Lateral trapping of DNA inside a voltage gated nanopore

The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic, fully three-dimensional setup as well as analytical approximations for a simplified model are worked out. By applying a suitable voltage to the membrane electrode, the DNA can be forced to preferably traverse the pore either along the pore axis or at a small but finite distance from the pore wall.

cond-mat.soft↗

arXiv2017

Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize

We consider isolated many-body quantum systems which do not thermalize, i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and XXZ models.

cond-mat.stat-mech↗

arXiv2016

Equilibration of isolated many-body quantum systems with respect to general distinguishability measures

We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are unimaginably rare in time. Measuring the distinguishability in terms of quantum mechanical expectation values, results of this type have been previously established under increasingly weak assumptions about the initial disequilibrium, the many-body Hamiltonian, and the considered observables. Here, we further extend these results with respect to generalized distinguishability measures which fully take into account the fact that the actually observed, primary data are not expectation values but rather the probabilistic occurrence of different possible measurement outcomes.

cond-mat.stat-mech↗

arXiv2016

Typical fast thermalization processes in closed many-body systems

Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a very successful general framework to cope with this problem. Far from equilibrium, only very few quantitative and comparably universal results are known. Here, a new quantum mechanical prediction of this type is derived and verified against various experimental and numerical data from the literature. It quantitatively describes the entire temporal relaxation towards thermal equilibrium for a large class (in a mathematically precisely defined sense) of closed many-body systems, whose initial state may be arbitrarily far from equilibrium.

cond-mat.stat-mech↗

arXiv2015

Generalization of von Neumann's Approach to Thermalization

Thermalization of isolated many-body systems is demonstrated by generalizing an approach originally due to von Neumann: For arbitrary initial states with a macroscopically well-defined energy, quantum mechanical expectation values become indistinguishable from the corresponding microcanonical expectation values for the overwhelming majority of all sufficiently late times. As in von Neumann's work, the eigenvectors of the Hamiltonian and of the considered observable are required to not exhibit any specially tailored (untypical) orientation relative to each other. But all of von Neumann's further assumptions about the admitted observables are abandoned.

cond-mat.stat-mech↗

arXiv2015

Eigenstate thermalization: Deutsch's approach and beyond

The eigenstate thermalization hypothesis (ETH) postulates that the energy eigenstates of an isolated many-body system are thermal, i.e., each of them already yields practically the same expectation values as the microcanonical ensemble at the same energy. Here, we review, compare, and extend some recent approaches to corroborate this hypothesis and discuss the implications for the system's equilibration and thermalization.

cond-mat.stat-mech↗

arXiv2014

Reluctance of a neutral nanoparticle to enter a charged pore

We consider the translocation of a neutral (uncharged) nanoparticle through a pore in a thin membrane with constant surface charge density. If the concomitant Debye screening layer is sufficiently thin, the resulting forces experienced by the particle on its way through the pore are negligible. But when the Debye length becomes comparable to the pore diameter, the particle encounters a quite significant potential barrier while approaching and entering the pore, and symmetrically upon exiting the pore. The main reason is an increasing pressure which acts on the particle when it intrudes into the counter ion cloud of the Debye screening layer. In case the polarizability of the particle is different (usually smaller) than that of the ambient fluid, a second, much smaller contribution to the potential barrier is due to self-energy effects. Our numerical treatment of the problem is complemented by analytical approximations for sufficiently long cylindrical particles and pores, which agree very well with the numerics.

cond-mat.soft↗

arXiv2013

On the Foundation of Statistical Mechanics under Experimentally Realistic Conditions: A Comparison between the Quantum and the Classical Case

Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior ("equilibration")? In how far is this steady state in agreement with the microcanonical ensemble as predicted by Statistical Mechanics ("thermalization")? In the first part of the paper, a recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and non-equilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. In the second part, an analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.

cond-mat.stat-mech↗

arXiv2013

Opposite translocation of long and short oligomers through a nanopore

We consider elongated cylindrical particles, modeling e.g. DNA fragments or nano-rods, while translocating under the action of an externally applied voltage through a solid state nanopore. Particular emphasis is put on the concomitant potential energy landscape, encountered by the particle on its passage through the pore due to the complex interplay of various electrohydrodynamic effects beyond the realm of small Debye lengths. We find that the net potential energy difference across the membrane may be of opposite sign for short and long particles of equal diameters and charge densities (e.g. oligomers). Thermal noise thus leads to biased diffusion through the pore into opposite directions. By means of an additional membrane gate electrode it is even possible to control the specific particle length at which this transport inversion occurs.

cond-mat.soft↗

arXiv2012

Equilibration of Isolated Macroscopic Quantum Systems under Experimentally Realistic Conditions

In how far does an non-equilibrium initial ensemble evolve towards a stationary long time behavior for an isolated macroscopic quantum system? We demonstrate that deviations from a steady state indeed become unmeasurably small or exceedingly rare after initial transients have died out under the following conditions: The Hamilonian does not exhibit exceedingly large degeneracies of energy eigenvalues and energy gaps. A large number of energy levels is significantly populated by the initial ensemble. The system is observed by a measurement device with a reasonably bound working range compared to the resolution limit. The entire experiment, ending with the quantum mechanical measurement process, can only be repeated a "reasonable" number of times. It is argued that all these prerequisites for equilibration are fulfilled under many, if not all, experimentally realistic conditions.

cond-mat.stat-mech↗

arXiv2012

Chiral particle separation by a non-chiral micro-lattice

We conceived a model experiment for a continuous separation strategy of chiral molecules (enantiomers) without the need of any chiral selector structure or derivatization agents: Micro-particles that only differ by their chirality are shown to migrate along different directions when driven by a steady fluid flow through a square lattice of cylindrical posts. In accordance with our numerical predictions, the transport directions of the enantiomers depend very sensitively on the orientation of the lattice relatively to the fluid flow.

cond-mat.stat-mech↗

arXiv2012

On the Lubensky-Nelson model of polymer translocation through nanopores

We revisit the one-dimensional stochastic model of Lubensky and Nelson [Biophys. J 77, 1824 (1999)] for the electrically driven translocation of polynucleotides through alpha-hemolysin pores. We show that the model correctly describes two further important properties of the experimentally observed translocation time distributions, namely their spread (width) and their exponential decay. The resulting overall agreement between theoretical and experimental translocation time distributions is thus very good.

physics.bio-ph↗