Analytical continuation approaches to electronic transport: The resonant level model

Wilner, Eli Y.; Levy, Tomer; Rabani, Eran

doi:10.1063/1.4768674

Cited by 3 publications

(4 citation statements)

References 58 publications

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“…Notably, this model has been long known to be exactly solvable 44 and features in textbooks on quantum transport and electron transfer 45 . However, we will see that this does not 46,47 imply this problem is fully understood, even though we do not address the role of Coulomb interactions responsible for various manybody effects in transport measurements 43 . These aspects are certainly important but beyond the present scope.…”

Section: Level-occupation N(t)mentioning

confidence: 92%

“…Finally, we construct the density matrix (47) of the effective environment ρ E ′ (t) kk ′ ηη ′ := Tr S K k η (t)ρ(0)K k ′ η ′ (t) † and first focus on the odd-and even-parity diagonal blocks k = k ′ that remain when the initial system state ρ(0) obeys superselection. The odd block (k = 1) is already diagonal in this basis,…”

Section: Effective Environment Density Matrixmentioning

confidence: 99%

“…Above and in the main text [Eq. (47)] we claimed that the off-diagonal blocks of ρ E ′ (t) are zero for all t ≥ 0 if ρ(0) obeys superselection, i.e., d(0) = 0. An explicit calculation of the off-diagonal blocks…”

Section: Pseudo-spin Model Without Superselectionmentioning

confidence: 99%

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Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

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To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.

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Section: Level-occupation N(t)mentioning

confidence: 92%

Section: Effective Environment Density Matrixmentioning

confidence: 99%

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Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Reimer

Wegewijs

Nestmann

et al. 2019

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Since its original formulation in 1948, , Feynman’s space–time approach to nonrelativistic quantum mechanics (known as ‘path integral’ or ‘sum over histories’) has provided a powerful tool for studying many-body problems at finite temperatures without introducing uncontrolled approximations. − While computing thermodynamic properties of homogeneous quantum fluids (in this study “quantum fluids” are restricted to fluids composed of Boltzmannons) at finite temperatures via path integral has become routine, , the calculation of thermodynamic properties of an open isothermal system (i.e., a system that can exchange both heat energy and quantum particles with its surroundings) remains a challenging problem in computational chemistry. Adsorption of light particles (i.e., hydrogen isotopes, light noble gases, and light alkanes) in nanoporous materials at cryogenic temperatures is a typical example, where the simulation in an open system offers a natural framework for calculation of basic thermodynamic functions (i.e., the amount of adsorbed fluid, the enthalpy accompanying the adsorption processes, etc.…”

Section: Introductionmentioning

confidence: 99%

Constant Pressure Path Integral Gibbs Ensemble Monte Carlo Method

Kowalczyk

Gauden²,

Terzyk³

et al. 2013

J. Chem. Theory Comput.

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We present the implementation of a real-space constant pressure path integral Gibbs ensemble Monte Carlo (CP-PIGEMC) method for the simulation of one-component fluid consists of distinguishable quantum particles (henceforth referred to as Boltzmannons) in an external potential field at finite temperatures. We apply this simulation method to study the para-H2 adsorption in NaX zeolite at 77 K and pressures up to 100 bar. We present a new set of effective solid-fluid parameters optimized for path integral simulations of hydrogen isotope adsorption and separation in synthetic zeolites. The agreement among CP-PIGEMC, experiment, and the path integral grand canonical Monte Carlo method (PIGCMC) is very good, even at high pressures. CP-PIGEMC is a particularly useful method for simulation of one-component quantum fluid composed of Boltzmannons at finite temperatures, when the chemical potential is difficult to measure or calculate explicitly.

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Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

Levy

Rabani

2013

The Journal of Chemical Physics

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We study steady state transport through a double quantum dot array using the equation-ofmotion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations, however its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results. This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.

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Analytical continuation approaches to electronic transport: The resonant level model

Cited by 3 publications

References 58 publications

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

Constant Pressure Path Integral Gibbs Ensemble Monte Carlo Method

Steady state conductance in a double quantum dot array: The nonequilibrium equation-of-motion Green function approach

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