Lefschetz-thimble inspired analysis of the Dykhne–Davis–Pechukas method and an application for the Schwinger Mechanism

Fukushima, Kenji; Shimazaki, Takuya

doi:10.1016/j.aop.2020.168111

Cited by 12 publications

(12 citation statements)

References 39 publications

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“…It is possible to reformulate equation ( 30) by changing to the variable x ∈ (−∞, +∞), where t = tanh(x), and dt/(t 2 − 1) = dx. This makes it standard for application of the, so-called, Dykhne formula for the overgap transition probability between two states [35,36] in the adiabatic limit, in which overgap transitions are suppressed exponentially. This formula provides the corresponding slowest decaying exponent and its leading order prefactor.…”

Section: A Symmetric Modelmentioning

confidence: 99%

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Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

2021

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We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a qaudratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-Stückelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly-looking models belong to different topological classes.

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Section: A Symmetric Modelmentioning

confidence: 99%

“…where φ g is a geometric phase difference between the two trajectories. It is of subdominant order O(1) in comparison to the integrals in (35), and for real Hamiltonians can take only discrete values 0 or π. In appendix A, we calculate this phase for both H 1 and H 2 and show that for the symmetric model φ g = 0.…”

Section: A Symmetric Modelmentioning

confidence: 99%

Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

2021

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“…In the adiabatic limit, this solution becomes asymptotically exact. Namely, the Dykhne formula 16 provides the over-gap transition probability:…”

Section: The Transition Probabilities In the Adiabatic Limitmentioning

confidence: 99%

Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

Chernyak¹,

Sinitsyn²

2020

Preprint

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Exactly solvable multistate Landau-Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. We show how such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New fully solvable MLZ systems are also found.where B 0 , B 1 , A and C are real symmetric (t, τ )independent matrices, such that the Hamiltonians (4) and ( 5) satisfy the integrability conditions (2) and (3) for two time-like variables, τ 1 = t and τ 2 = τ . Even

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“…As we need to construct the Green's function G R 0 , we have to calculate a + (t) at generic time t as opposed to the conventional tunneling problem where one considers only the t → ∞ limit. According to the Lefschetz thimble approach recently proposed for the tunneling problem [54], the asymptotic form for the nonperturbative component should be given as…”

Section: A Overviewmentioning

confidence: 99%

“…The central issue here is that we have to compute a + (t) as a function of t, which is in contrast to the conventional tunneling problem discussing the t → ∞ limit. We first discuss this using the Lefschetz thimble approach [54]. Then we construct G R 0 (t, t ′ ) with the tunneling correction and derive the formula for G < (t, t ′ ).…”

Section: Tunneling Contributionmentioning

confidence: 99%

Current response of nonequilibrium steady states in Landau-Zener problem: Nonequilibrium Green's function approach

Kitamura,

Nagaosa,

Morimoto

2020

Preprint

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The carrier generation in insulators subjected to strong electric fields is characterized by the Landau-Zener formula for the tunneling probability with a nonperturbative exponent. Despite its long history with diverse applications and extensions, study of nonequilibrium steady states and associated current response in the presence of the generated carriers has been mainly limited to numerical simulations so far. Here, we develop a framework to calculate the nonequilibrium Green's function of generic insulating systems under a DC electric field, in the presence of a fermionic heat bath. Using asymptotic expansion techniques, we derive a semi-quantitative formula for the Green's function with nonperturbative contribution. This formalism enables us to calculate dissipative current response of the nonequilibrium steady state, which turns out to be not simply characterized by the intraband current proportional to the tunneling probability. We also apply the present formalism to noncentrosymmetric insulators, and propose nonreciprocal charge and spin transport peculiar to tunneling electrons.

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Lefschetz-thimble inspired analysis of the Dykhne–Davis–Pechukas method and an application for the Schwinger Mechanism

Cited by 12 publications

References 39 publications

Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

Nonadiabatic transitions in Landau-Zener grids: Integrability and semiclassical theory

Integrability in the multistate Landau-Zener model with time-quadratic commuting operators

Current response of nonequilibrium steady states in Landau-Zener problem: Nonequilibrium Green's function approach

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