scholarly journals Dissipative linear response theory and its appications in open quantum systems

2021 ◽  
Vol 70 (23) ◽  
pp. 1-11
Author(s):  
Chen Yu ◽  
Keyword(s):  
Linear Response ◽  
Open Quantum Systems ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Response Theory ◽  
Open Quantum

scholarly journals A Generalised Linear Response Theory applied to the Dielectric Function of Coulomb Systems

2000 ◽  
Vol 53 (1) ◽  
pp. 133 ◽  
Author(s):  
H. Reinholz
Keyword(s):  
Dielectric Function ◽  
Linear Response ◽  
Electron Gas ◽  
Three Dimensional ◽  
Coulomb Systems ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Response Theory ◽  
Long Wavelength ◽  
Wave Numbers

A generalised linear response theory is used to derive the dielectric function at arbitrary wave numbers k and frequencies w for interacting quantum systems. The connection to thermodynamic Green functions allows the systematic perturbative treatment going beyond RPA and treating local field corrections as well as the inclusion of collisions on the same footing. Emphasis will be on the demonstration of the formalism. Results will be presented for the three-dimensional as well as two-dimensional case of an interacting electron gas. In the long-wavelength limit, a Drude-type expression with frequency dependent relaxation time is given bridging the theories of dielectric function and electrical conductivity.

scholarly journals Quantized classical response from spectral winding topology

2021 ◽  
Author(s):  
Linhu Li ◽  
Sen Mu ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Linear Response ◽  
Condensed Matter ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Topological Invariants ◽  
Response Theory ◽  
New Paradigm ◽  
Classical Systems ◽  
State Response ◽  
Mathematical Properties

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.

scholarly journals Quantized classical response from spectral winding topology

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Linhu Li ◽  
Sen Mu ◽  
Ching Hua Lee ◽  
Jiangbin Gong
Keyword(s):  
Linear Response ◽  
Linear Response Theory ◽  
Quantum Systems ◽  
Topological Invariants ◽  
Edge States ◽  
Response Theory ◽  
New Paradigm ◽  
Classical Systems ◽  
State Response ◽  
Mathematical Properties

AbstractTopologically 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 states 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.

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