Time-loop formalism for irreversible quantum problems : Steady-state transport in junctions with asymmetric dynamics

@article{Kakashvili2008TimeloopFF,
  title={Time-loop formalism for irreversible quantum problems : Steady-state transport in junctions with asymmetric dynamics},
  author={Paata Kakashvili and Carlos Bolech},
  journal={Physical Review B},
  year={2008},
  volume={78}
}
Non-unitary quantum mechanics has been used in the past to study irreversibility, dissipation and decay in a variety of physical systems. In this letter, we propose a general scheme to deal with systems governed by non-Hermitian Hamiltonians. We argue that the Schwinger-Keldysh formalism gives a natural description for those problems. To elucidate the method, we study a simple model inspired by mesoscopic physics --an asymmetric junction. The system is governed by a non-Hermitian Hamiltonian… 

Figures from this paper

Steady‐state non‐equilibrium transport in non‐Hermitian open quantum nanostructures
We present two classic case studies of non‐equilibrium transport from the mesoscopics literature, – a single‐channel tunneling junction and a tunneling junction with an embedded resonant level –,
Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point
Following the development of a scheme to bosonize and debosonize consistently [N. Shah and C.J. Bolech, Phys. Rev B 93, 085440 (2016); arXiv:1508.03078], we present in detail the Toulouse-point
Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle
We critically reexamine the bosonization-debosonization procedure for systems including certain types of localized features (although more general scenarios are possible). By focusing on the case of
Quantum/Relativistic Computation of Security and Efficiency of Electrical Power System for a Day-Ahead: I. Renormalization
An algorithm for Electric Power System (EPS) quantum/relativistic security and efficiency computation for a day-ahead via perturbative renormalization of the EPS, finding the computation flowcharts,

References

SHOWING 1-10 OF 29 REFERENCES
Localization Transitions in Non-Hermitian Quantum Mechanics.
TLDR
The theory predicts that, close to the depinning transition, the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth.
Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation.
  • Gwa, Spohn
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1992
We approximate the noisy Burgers equation by the single-step model, alias the asymmetric simple exclusion process. The generator of the corresponding master equation is identical to the ferromagnetic
Vortex pinning and non-Hermitian quantum mechanics
A delocalization phenomenon is studied in a class of non-Hermitian random quantum-mechanical problems. Delocalization arises in response to a sufficiently large constant imaginary vector potential.
Brownian Motion of a Quantum Oscillator
An action principle technique for the direct computation of expectation values is described and illustrated in detail by a special physical example, the effect on an oscillator of another physical
A DMRG study of the -symmetric Heisenberg chain
Abstract:The spin one-half Heisenberg chain with Uq[SU(2)] symmetry is studied via density-matrix renormalization. Ground-state energy and q-symmetric correlation functions are calculated for the
Time-dependent transport in interacting and noninteracting resonant-tunneling systems.
TLDR
Analytical and numerical results for the exactly solvable noninteracting resonant-tunneling system are presented, and a connection to recent linear-response calculations, and to earlier studies of electron-phonon scattering effects in resonant tunneling is established.
Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
The breakdown of the Mott insulator is studied when the dissipative tunneling into the environment is introduced to the system. By exactly solving the one-dimensional asymmetric Hubbard model, we
Microphysical irreversibility and the time-reversal operation.
  • Bohm
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1995
The division of a scattering experiment into the preparation of a state and the registration of an observable in this state defines an obvious but commonly ignored quantum-mechanical arrow of time.
Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments.
TLDR
A model Hamiltonian is introduced that describes the tunneling process when electrons are injected into zero-energy bound states of chiral p-wave superconductors and exact analytic expressions for tunneling current and noise are found and experimental signatures of the Majorana nature of the bound states are identified in the shot noise.
Density matrix renormalization group and reaction-diffusion processes
Abstract:The density matrix renormalization group ( DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity of and at their critical point. The stochastic time evolution
...
1
2
3
...