Physical Phenomena in Semiconductors With Negative Differential Conductivity

Volkov, A. N.; Kogan, Sh. M.

doi:10.1070/pu1969v011n06abeh003780

Cited by 191 publications

(239 citation statements)

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“…In these problems the goal is to describe the dynamics of a many-body system following a sudden perturbation that drove the system out of an equilibrium. The system in question can be a BCS superconductor [1,2,3,4,5,6,7,8,9,10,11], coupled FermiBose condensates [12,13], or a single electronic spin interacting with many nuclear spins (the central spin model) [14,15,16,17,18,19,20]. A common feature of all these problems is that they can be formulated in terms of spin Hamiltonians, which belong to a class of integrable systems known as Gaudin magnets [21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Integrable dynamics of coupled Fermi-Bose condensates

2005

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We study the mean-field dynamics of a fermionic condensate interacting with a single bosonic mode (a generalized Dicke model). This problem is integrable and can be mapped onto a corresponding BCS problem. We derive the general solution and a full set of integrals of motion for the time evolution of coupled Fermi-Bose condensates. The present paper complements our earlier study of the dynamics of the BCS model (cond-mat/0407501 and cond-mat/0505493). Here we provide a self-contained introduction to the variable separation method, which enables a complete analytical description of the evolution of the generalized Dicke, BCS, and other similar models.

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Section: Introductionmentioning

confidence: 99%

Integrable dynamics of coupled Fermi-Bose condensates

2005

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“…In terms of F m (t) = 2is z m and G m (t) = 2is − m , Green's functions at coinciding times, Eqs. (20) are well-known Gorkov equations [24,46]. The above procedure leading to Gorkov equations is essentially equivalent to taking the time-dependent wave function of the system to have the product form (2) at all times.…”

Section: A Notations and Basic Equationsmentioning

confidence: 99%

“…The dissipationless dynamics of a fermionic superfluid can be modeled by the reduced BCS Hamiltonian [24,25,27,38]…”

Section: A Notations and Basic Equationsmentioning

confidence: 99%

“…This presents a significant challenge as conventional techniques are often inadequate for the description of these phenomena. In particular, there have been major advances in the theory of dynamical fermionic pairing in the collisionless regime [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. This problem is long known to be accurately described by the time-dependent Bogoliubov-de Gennes equations, which in this case are a set of coupled nonlinear integro-differential equations [24,25,27,30].…”

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confidence: 99%

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Normal and anomalous solitons in the theory of dynamical Cooper pairing

Yuzbashyan

2008

Phys. Rev. B

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We obtain multi-soliton solutions of the time-dependent Bogoliubov-de Gennes equations or, equivalently, Gorkov equations that describe the dynamics of a fermionic condensate in the dissipationless regime. There are two kinds of solitons -normal and anomalous. At large times, normal multi-solitons asymptote to unstable stationary states of the BCS Hamiltonian with zero order parameter (normal states), while the anomalous ones tend to eigenstates characterized by a nonzero anomalous average. Under certain circumstances, multi-soliton solutions break up into sums of single solitons. In the linear analysis near the stationary states, solitons correspond to unstable modes. Generally, they are nonlinear extensions of these modes, so that a stationary state with k unstable modes gives rise to a k-soliton solution. We relate parameters of the multi-solitons to those of the asymptotic stationary state, which determines the conditions necessary for exciting solitons. We further argue that the dynamics in many physical situations is multi-soliton.

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“…In this situation we must return to the Gorkov equations describing the mean-field dynamics of the individual Cooper pairs [12]. We study here only the limit in which dissipative processes are neglected (τ → ∞) and the dynamics controlled purely by the BCS Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Dissipationless BCS dynamics with large branch imbalance

Nahum

Bettelheim

2008

Phys. Rev. B

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In many situations a BCS-type superconductor will develop an imbalance between the populations of the hole-like and electron-like spectral branches. This imbalance suppresses the gap. It has been noted by Gal'perin, Kozub and Spivak [6] that at large imbalance, when the gap is substantially suppressed, an instability develops. The analytic treatment of the system beyond the instability point is complicated by the fact that the Boltzmann approach breaks down. We study the short time behavior following the instability, in the collisionless regime, using methods developed by Yuzbashyan et al. [18,19].

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Physical Phenomena in Semiconductors With Negative Differential Conductivity

Cited by 191 publications

References 1 publication

Integrable dynamics of coupled Fermi-Bose condensates

Integrable dynamics of coupled Fermi-Bose condensates

Normal and anomalous solitons in the theory of dynamical Cooper pairing

Dissipationless BCS dynamics with large branch imbalance

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