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.The long-standing task to explain macroscopic equilibration phenomena in terms of the underlying microscopic quantum dynamics is presently regaining considerable attention [1][2][3]. Since open systems are beyond the realm of standard quantum mechanics, the common starting point is an isolated many-body system, possibly incorporating the environment of the subsystem of actual interest. The question whether and how such a system or subsystem approaches some thermal or nonthermal equilibrium state after a sufficiently long time has been at the focus of numerous analytical [4][5][6], numerical [7][8][9][10][11][12], and experimental [13][14][15][16][17][18] studies. Despite the reversible and everlasting motion of the microscopic degrees of freedom, it could be shown in Refs. [19,20] under increasingly weak assumptions about the system Hamiltonian, the initial condition, and the considered observable that expectation values must remain extremely close to a constant value for the vast majority of all sufficiently late times (the exceptional times include initial transients and quantum revivals).The natural next question is whether the system thermalizes, that is, whether the longtime behavior is well approximated by the pertinent microcanonical expectation value from equilibrium statistical mechanics. A first prominent criterion for thermalization is the so-called eigenstate thermalization hypothesis (ETH), postulating that every energy eigenstate yields expectation values close to the corresponding microcanonical values [5][6][7][8].In other words, a violation of ETH is commonly considered an indicator of nonthermalization [1,[6][7][8][9]. A related but different such indicator is the existence of additional conserved quantities (besides the system Hamiltonian) which can be written as sums of local operators, and which play a particularly prominent role for so-called integrable systems [1]. Numerically, it has been found that such systems usually violate the ETH and do not thermalize [7][8][9]. Instead, the longtime behavior is well captured by a so-called generalized Gibbs ensemble (GGE), which is obtained by the standard working recipe to maximize the von Neumann entropy under the constraints that the expectation values of the conserved quantities must be correctly reproduced [7]. Yet another commo...

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.

Surface-enhanced Raman scattering (SERS) is a promising analytical technique for the detection and characterization of biological molecules and structures. The role of hydrophobic and hydrophilic surfaces in the self-assembly of protein-metallic nanoparticle structures for label-free protein detection is demonstrated. Aggregation is driven by both the hydrophobicity of the surface as well as the charge of the proteins. The best conditions for obtaining a reproducible SERS signal that allows for sensitive, label-free protein detection are provided by the use of hydrophobic surfaces and 16 × 10(11) NPs per mL. A detection limit of approximately 0.5 μg mL(-1) is achieved regardless of the proteins' charge properties and size. The developed method is simple and can be used for reproducible and sensitive detection and characterization of a wide variety of biological molecules and various structures with different sizes and charge status.

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schrödinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool.