Quantized classical response from spectral winding topology

• URL: http://arxiv.org/abs/2012.08799v2
• Date: Tue, 16 Feb 2021 14:07:44 GMT
• Title: Quantized classical response from spectral winding topology
• Authors: Linhu Li, Sen Mu, Ching Hua Lee, Jiangbin Gong
• Abstract summary: Topologically quantized response is one of the focal points of contemporary condensed matter physics. We discover a new paradigm of quantized classical response based on the spectral winding number in the complex spectral plane. The ratio of the change in one quantity depicting amplification signal to the variation in one imaginary flux-like parameter is found to display fascinating plateaus.
• Score: 2.8522243039930557
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge modes as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green's function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

Related papers

• Quantum recurrences in the kicked top [1.1470070927586016]
  We present an infinite family of quantum dynamics that never resembles the analogous classical chaotic dynamics irrespective of dimension. Because these state-independent temporal periodicities are present in all dimensions, their existence represents a universal violation of the correspondence principle. We discuss the relationship of these periodicities with the quantum kicked rotor, in particular the phenomenon of quantum anti-resonance.
  arXiv  Detail & Related papers  (2023-07-30T23:42:24Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• The wave operator representation of quantum and classical dynamics [0.0]
  We study the little-known wave operator representation of quantum dynamics. We find it leads to novel semiclassical approximations of both real and imaginary time dynamics. We argue that the wave operator provides a new perspective that links previously unrelated representations.
  arXiv  Detail & Related papers  (2023-02-26T02:21:31Z)
• A linear response framework for simulating bosonic and fermionic correlation functions illustrated on quantum computers [58.720142291102135]
  Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. Within the context of quantum computing, we make the experiment an inextricable part of the quantum simulation. We show that both bosonic and fermionic Green's functions can be obtained, and apply these ideas to the study of a charge-density-wave material.
  arXiv  Detail & Related papers  (2023-02-20T19:01:02Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators [0.0]
  Self-oscillating systems are emerging as canonical models for driven dissipative nonequilibrium open quantum systems. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature.
  arXiv  Detail & Related papers  (2020-11-05T08:51:51Z)
• Classical limit of quantum mechanics for damped driven oscillatory systems: Quantum-classical correspondence [0.0]
  We develop a quantum formalism on the basis of a linear-invariant theorem. We illustrate the correspondence of the quantum energy with the classical one in detail.
  arXiv  Detail & Related papers  (2020-10-18T12:12:01Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

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.