Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
- URL: http://arxiv.org/abs/2408.05343v1
- Date: Fri, 26 Jul 2024 15:20:07 GMT
- Title: Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
- Authors: Nadav Shaibe, Jared M. Erb, Steven M. Anlage,
- Abstract summary: Wigner-Smith time-delay of flux conserving systems is a quantity that measures how long an excitation resides in an interaction region.
We calculate the complex Wigner-Smith ($tau_WS$), as well as each individual reflection ($tau_xx$) and transmission ($tau_xy$) time-delays.
The time-delay statistics described in this paper are applicable to any non-Hermitian wave-chaotic scattering system in the short-wavelength limit.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Wigner-Smith time-delay of flux conserving systems is a real quantity that measures how long an excitation resides in an interaction region. The complex generalization of time-delay to non-Hermitian systems is still under development, in particular, its statistical properties in the short-wavelength limit of complex chaotic scattering systems has not been investigated. From the experimentally measured multi-port scattering ($S$)-matrices of one-dimensional graphs, a two-dimensional billiard, and a three-dimensional cavity, we calculate the complex Wigner-Smith ($\tau_{WS}$), as well as each individual reflection ($\tau_{xx}$) and transmission ($\tau_{xy}$) time-delays. The complex reflection time-delay differences ($\tau_{\delta R}$) between each port are calculated, and the transmission time-delay differences ($\tau_{\delta T}$) are introduced for systems exhibiting non-reciprocal scattering. Large time-delays are associated with coherent perfect absorption, reflectionless scattering, slow light, and uni-directional invisibility. We demonstrate that the large-delay tails of the distributions of the real and imaginary parts of each of these time-delay quantities are superuniversal, independent of experimental parameters: uniform attenuation $\eta$, number of scattering channels $M$, wave propagation dimension $\mathcal{D}$, and Dyson symmetry class $\beta$. This superuniversality is in direct contrast with the well-established time-delay statistics of unitary scattering systems, where the tail of the $\tau_{WS}$ distribution depends explicitly on the values of $M$ and $\beta$. Due to the direct analogy of the wave equations, the time-delay statistics described in this paper are applicable to any non-Hermitian wave-chaotic scattering system in the short-wavelength limit, such as quantum graphs, electromagnetic, optical and acoustic resonators, etc.
Related papers
- Universal Spreading Dynamics in Quasiperiodic Non-Hermitian Systems [4.350531579293999]
Non-Hermitian systems exhibit a distinctive type of wave propagation, due to the intricate interplay of non-Hermiticity and disorder.
We investigate the spreading dynamics in the archetypal non-Hermitian Aubry-Andr'e model with quasiperiodic disorder.
arXiv Detail & Related papers (2024-12-02T09:13:43Z) - Information scrambling and entanglement dynamics in Floquet Time Crystals [49.1574468325115]
We study the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement of entropy as measures of information propagation in disordered systems.
arXiv Detail & Related papers (2024-11-20T17:18:42Z) - Dynamical formulation of low-frequency scattering in two and three dimensions [0.0]
Theory of scattering in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system.
In two and three dimensions, there is a similar formulation of stationary scattering where the scattering properties of the scatterer are extracted from the evolution operator.
We obtain explicit formulas for low-frequency scattering amplitude, examine their effectiveness in the study of a class of exactly solvable scattering problems, and outline their application in devising a low-frequency cloaking scheme.
arXiv Detail & Related papers (2024-10-22T11:26:58Z) - Inclusive reactions from finite Minkowski spacetime correlation functions [44.99833362998488]
We use real-time methods to determine scattering amplitudes of few-hadron systems for arbitrary kinematics.
In units of the lightest mass of the theory, we find that to constrain amplitudes using real-time methods within $mathcalO(10%)$, the spacetime volumes must satisfy $mL sim mathcalO(10-102)$ and $ mTsim mathcalO(102-104)$.
arXiv Detail & Related papers (2024-06-11T01:39:24Z) - Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos [0.0]
We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos.
We find that the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state.
We conjecture that the thermofield double state (TFD) is suitable for probing signatures of chaos in quantum many-body systems.
arXiv Detail & Related papers (2024-05-18T10:54:50Z) - Temporal fluctuations of correlators in integrable and chaotic quantum
systems [0.0]
We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies.
For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size.
arXiv Detail & Related papers (2023-07-17T12:35:38Z) - Local-Global Temporal Difference Learning for Satellite Video
Super-Resolution [55.69322525367221]
We propose to exploit the well-defined temporal difference for efficient and effective temporal compensation.
To fully utilize the local and global temporal information within frames, we systematically modeled the short-term and long-term temporal discrepancies.
Rigorous objective and subjective evaluations conducted across five mainstream video satellites demonstrate that our method performs favorably against state-of-the-art approaches.
arXiv Detail & Related papers (2023-04-10T07:04:40Z) - Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications.
We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
arXiv Detail & Related papers (2023-01-18T11:29:49Z) - On Statistical Distribution for Adiabatically Isolated Body [62.997667081978825]
The statistical distribution for the case of an adiabatically isolated body was obtained in the framework of covariant quantum theory.
The energy of an isolated system is an external parameter for the modified distribution instead of temperature.
arXiv Detail & Related papers (2022-05-15T09:33:36Z) - Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling.
In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures.
By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
arXiv Detail & Related papers (2022-02-14T02:23:16Z) - Non-Markovian anti-parity-time symmetric systems: theory and experiment [0.0]
We show that a single time-delay encodes the memory, and experimentally demonstrate its consequences with two time-delay coupled semiconductor lasers.
We show that a sequence of amplifying-to-decaying dominant mode transitions is induced by the time delay in our minimal model.
Our work introduces a new paradigm of non-Hermitian systems with memory, paves the way for their realization in classical systems, and may apply to time-delayed feedback-control for quantum systems.
arXiv Detail & Related papers (2022-01-13T05:17:08Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.