An empirical interpretation for the time evolution of the Caii K line

The historical development of kinetic theory is reviewed with respect to the inclusion of virial corrections. Here the theory of dense gases differs from quantum liquids. While the first one leads to Enskog-type of corrections to the kinetic theory, the latter ones are described by quasiparticle concepts of Landau-type theories. A unifying kinetic theory is envisaged by the nonlocal quantum kinetic theory. Nonequilibrium phenomena are the essential processes which occur in nature. Any evolution is built up of involved causal networks which may render a new state of quality in the course of time evolution. The steady state or equilibrium is rather the exception in nature, if not a theoretical abstraction at all.

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Time evolution of chaotic quantum systems

Annals of Physics ◽

10.1016/0003-4916(92)90354-o ◽

1992 ◽

Vol 219 (2) ◽

pp. 364

Keyword(s):

Time Evolution ◽

Quantum Systems

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The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

Journal of High Energy Physics ◽

10.1007/jhep02(2021)129 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Sébastien Descotes-Genon ◽

Martín Novoa-Brunet ◽

K. Keri Vos

Keyword(s):

Time Evolution ◽

Form Factors ◽

New Physics ◽

Time Dependent ◽

Angular Analysis ◽

Time Dependent Analysis ◽

Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

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Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

Physical Chemistry Chemical Physics ◽

10.1039/d0cp05528j ◽

2021 ◽

Author(s):

Sambarta Chatterjee ◽

Nancy Makri

Keyword(s):

Density Matrix ◽

Time Evolution ◽

Reduced Density Matrix ◽

Level System ◽

Two Level Systems ◽

Reduced Density ◽

Harmonic Bath

We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates.

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Complexity growth in integrable and chaotic models

Journal of High Energy Physics ◽

10.1007/jhep07(2021)011 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Vijay Balasubramanian ◽

Matthew DeCross ◽

Arjun Kar ◽

Yue Li ◽

Onkar Parrikar

Keyword(s):

Time Evolution ◽

Evolution Operator ◽

Linear Growth ◽

Conjugate Points ◽

Majorana Fermions ◽

Time Evolution Operator ◽

Free Theory ◽

Group Manifold ◽

Geodesic Length ◽

Evolution Trajectory

Abstract We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($$ \sqrt{N} $$ N ), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(eN), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

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