D. Taubert, C. Tomaras, G. J. Schinner, H. P. Tranitz, W. Wegscheider, S. Kehrein, and S. Ludwig
Relaxation of hot electrons in a degenerate two-dimensional electron system: transition to one-dimensional scattering
arXiv:1104.1645, Phys. Rev. B 83, 235404 (2011)
The energy relaxation channels of hot electrons far from thermal equilibrium in a degenerate two-dimensional electron system are investigated in transport experiments in a mesoscopic three terminal device. We observe a transition from two dimensions at zero magnetic field to quasi-one-dimensional scattering of the hot electrons in a strong magnetic field. Theoretical calculations of electron-electron scattering and the emission of optical phonons underline our interpretation in terms of a transition to one-dimensional dynamics.
Atomic force micrograph of the Hall bar sample.
M. Heyl and S. Kehrein
The Crooks relation and its connection to the detailed balance principle of equilibrium correlation functions
Preprint arXiv:1012.2209
We show that in the quantum case any work distribution can be related to an equilibrium correlation function in an extended Hilbert space. As a consequence of this identification the Crooks relation is a restatement of the detailed balance principle for equilibrium correlation functions. The presented derivation serves as an alternative proof of the Crooks relation residing only on the detailed balance principle.
C. Tomaras and S. Kehrein
Scaling approach for the time-dependent Kondo model
arXiv:1011.1281, Eur. Phys. Lett. 93, 47011 (2011)
We develop a generalization of the flow equation method to time-dependent Hamiltonians. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale τ. The asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value.
Non-adiabacity of the interaction quench as a function of the time scale τ: Weak instantaneous quenches have μ=2, the adiabatic limit corresponds to μ=1.
M. Heyl and S. Kehrein
The X-ray edge singularity in quantum dots
Preprint arXiv:1007.3651
We investigate the X-ray edge singularity problem realized in noninteracting quantum dots. We analytically calculate the exponent of the singularity in the absorption spectrum near the threshold and extend known analytical results to the whole parameter regime. In particular, we verify the validity of the Hopfield rule of thumb in this exactly solvable nonequilibrium problem.
Possible experimental realization of x-ray edge physics in a noninteracting quantum dot.
P. Wang and S. Kehrein
Flow Equation Calculation of Transient and Steady State Currents in the Anderson Impurity Model
arXiv:1006.5203, Phys. Rev. B 82, 125124 (2010)
We present a new analytical approach based on the flow equation method for the calculation of transient and steady state currents in dc-biased quantum impurity models. Specifically, we analyze the Anderson impurity model in its mixed valence regime where the coupling to the leads is switched on suddenly at time t=0. We observe the real time buildup of the current until it reaches its steady state limit.
Real time buildup of the current beyond the linear response regime.
M. Heyl and S. Kehrein
The Crooks relation in optical spectra - universality in work distributions for weak local quenches
Preprint arXiv:1006.3522
We show that work distributions and non-equilibrium work fluctuation theorems can be measured in optical spectra for a big class of quantum systems. For the particular case of a weak local perturbation, the Crooks relation establishes a universal relation in absorption as well as in emission spectra. Due to a direct relation between the spectra and work distribution functions this is equivalent to universal relations in work distributions for weak local quenches. As two explicit examples we treat the X-ray edge problem and the Kondo exciton.
Crooks relation in the absorption spectrum of a Kondo exciton.
M. Eckstein, A. Hackl, S. Kehrein, M. Kollar, M. Moeckel, P. Werner, and F. A. Wolf
New theoretical approaches for correlated systems in nonequilibrium
arXiv:1005.5097, Eur. Phys. J. Special Topics 180, 217 (2010)
We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium, focussing mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations.
Fermi surface discontinuity after an interaction quench in the Hubard model. The prethermalization plateau is clearly visible.
V. Koerting, P. Fritsch, and S. Kehrein
Non-equilibrium Scaling Properties of a Double Quantum Dot System: Comparison between Perturbative Renormalization Group and Flow Equation Approach
arXiv:1004.1926, Physica B 406, 2091 (2011)
In this paper the differences and commons between the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.
Geometry of double dot system with four leads.
J. Rech and S. Kehrein
Measurement-backaction on adiabatic coherent electron transport
arXiv:1003.5743, Phys. Rev. Lett. 106, 136808 (2011)
We study the backaction of measurement on electrons undergoing coherent transfer via adiabatic passage (CTAP) in a triple-well system. We account for this continuous measurement by treating the whole {triple-well + detector} as a closed quantum system. This approach allows to study a single realization of the measurement process while keeping track of the detector output. As one increases the coupling between the middle potential well and the detector, one finds a substantial drop in the fidelity of the CTAP scheme.
Distribution of charges through QPC during CTAP protocol as a function of coupling strength D-D' of middle well to QPC.
P. Wang, M. Heyl and S. Kehrein
Exact results for nonlinear ac-transport through a resonant level model
arXiv:1003.3644, J. Phys. C 22, 275604 (2010)
We obtain exact results for the transport through a resonant level model for rectangular voltage bias as a function of time. We study both the transient behavior after switching on the tunneling and the ensuing steady state behavior. Among other effects, we observe current ringing and PAT (photon assisted tunneling) oscillations.
The steady state current in one period for intermediate fast driving.
M. Heyl, S. Kehrein, F. Marquardt, and C. Neuenhahn
Electron-Plasmon scattering in chiral 1D systems with nonlinear dispersion
arXiv:1002.2404, Phys. Rev. B 82, 033409 (2010)
We investigate systems of spinless one-dimensional chiral fermions occurring, e.g., in the arms of electronic Mach-Zehnder interferometers. We take into account the curvature of the fermionic spectrum and a finite interaction range. Due to an interplay of both, an injected high-energy electron can scatter off plasmons (density excitations) leading to an exponential decay of the single particle Green's function even at zero temperature. The excitation of plasmons leads to the buildup of a coherent monochromatic sinusoidal density pattern.
The fermionic density rho(x;t) in the co-moving frame of the high-energy electron.
D. Taubert, G. J. Schinner, H. P. Tranitz, W. Wegscheider, C. Tomaras, S. Kehrein, and S. Ludwig
An electron-avalanche amplifier based on the electronic Venturi effect
arXiv:1001.5201, Phys. Rev. B 82, 161416 (2010)
Ballistic transport of electrons far from equilibrium is investigated in a cold two-dimensional electron system. In a three-terminal device, we realize an electronic version of the Venturi effect that enables us to build an avalanche amplifier based on non-equilibrium electrons. This device might be developed further to create a non-invasive charge detector. A preliminary model based on numerical calculations using a random phase approximation is in agreement with our data.
Measured current characteristic of the 3-terminal device and current amplification region. The model for the electron-electron scattering length is based on an RPA approximation for the hot electrons.
M. Heyl and S. Kehrein
Interaction quench dynamics in the Kondo model in presence of a local magnetic field
arXiv:1001.2418, J. Phys. C 22, 345604 (2010)
We investigate the quench dynamics in the Kondo model on the Toulouse line in presence of a local magnetic field. The transient dynamics is studied by analyzing exact analytical results for the local spin dynamics. The time scale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.
Magnetization after an interaction quench in presence of an local magnetic field.
M. Heyl and S. Kehrein
Non-equilibrium steady state in a periodically driven Kondo model
arXiv:0911.2130, Phys. Rev. B 81, 144301 (2010)
We investigate the Kondo model with time-dependent couplings that are periodically switched on and off. On the Toulouse line we derive exact analytical results for the spin dynamics in the steady state that builds up after an infinite number of switching periods. In the limit of fast driving one can show that the steady state cannot be described by some effective equilibrium Hamiltonian since a naive implementation of the Trotter formula gives wrong results. As a consequence, the steady state in the limit of fast switching serves as an example for the emergence of new quantum states not accessible in equilibrium.
False color plot of the dynamical spin susceptibility for intermediate fast driving.
J. Sabio and S. Kehrein
Sudden interaction quench in the quantum sine-Gordon model
arXiv:0911.1302, New J. Phys. 12, 055008 (2010)
We study a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. We establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches.
Real time evolution of the bosonic mode occupation normalized by its equilibrium value for various momenta
M. Moeckel and S. Kehrein
Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
arXiv:0911.0875, New J. Phys. 12, 055016 (2010)
We investigate the crossover from adiabatic switching on of the interaction to sudden interaction quenches in a Fermi gas. The asymptotic momentum distribution function evolves from Landau's one to one mapping to a thermal distribution depending on the ramping speed. We obtain results for the effective temperature as a function of the ramping speed and establish the generic existence of a prethermalization regime.
Different time regimes for linear ramping and sudden interaction quenches in a Fermi gas.
P. Fritsch and S. Kehrein
Non-equilibrium Kondo model with voltage bias in a magnetic field
arXiv:0903.2865, Phys. Rev. B 81, 035113 (2010)
We derive a consistent 2-loop scaling picture for a Kondo dot in both equilibrium and non-equilibrium situations and calculate the spin-spin correlation function, the T-matrix and the magnetization as functions of voltage bias, temperature and magnetic field. In all these quantities we observe characteristic non-equilibrium features like Kondo splitting and strongly enhanced logarithmic corrections.
Splitting of the peak in the spectral function for a large magnetic field h=100TK due to a voltage bias as opposed to thermal smearing.
A. Hackl, M. Vojta, and S. Kehrein
Non-equilibrium magnetization dynamics of ferromagnetically coupled Kondo spins
arXiv:0908.3647, Phys. Rev. B 80, 195117 (2009)
An analytical description of non-equilibrium phenomena in interacting quantum systems is rarely possible. Here we present one example where such a description can be achieved, namely the ferromagnetic Kondo model. The flow equations admit analytical solutions which become exact at short and long times, in the latter case revealing that the system always retains a memory of its initial state.
Ratio r(g) of non-equilibrium vs. equilibrium expectation value as a function of the dimensionless coupling strength g.
M. Moeckel and S. Kehrein
Real-time evolution for weak interaction quenches in quantum systems
arXiv:0903.1561 [54 pages]; Ann. Phys. 324, 2146 (2009)
We investigate the real time evolution for weak interaction quenches in quantum many-body systems. Using simple systems like the squeezed harmonic oscillator we prove general statements relating time-averaged non-equilibrium expectation values to their equilibrium counterparts. We work out how this is related to thermalization after a sudden interaction quench in a Fermi gas, i.e. the opposite of Landau's adiabatic switching on procedure.
Figures (a) to (d):
Time evolution of the momentum distribution function after a sudden quench to ρU=0.6 in the Hubbard model.
Figure (e): Universal curves for equilibrium and the quasi-steady nonequilibrium state for small U.
A. Hackl, D. Roosen, S. Kehrein, and W. Hofstetter
Non-Equilibrium Spin Dynamics in the Ferromagnetic Kondo Model
arXiv:0903.1079, Phys. Rev. Lett. 102, 196601 (2009)
We study the real time dynamics of the impurity spin initially prepared in a product state with the bath for the ferromagnetic Kondo model. Both numerical time-dependent NRG and analytical flow equation calculations show a non-analytic spin decay that remarkably retains the memory of the initial preparation of the system for all times.
Spin decay for the isotropic ferromagnetic Kondo model. Crosses denote TD-NRG data points and squares are flow equation results.
P. Fritsch and S. Kehrein
Non–Equilibrium Scaling Analysis of the Kondo Model with Voltage Bias
arXiv:0811.0759, Ann. Phys. 324, 1105 (2009)
We work out a Hamiltonian scaling theory for the steady state of the Kondo model with voltage bias V. We focus on the spin dynamics and in particular on the static spin susceptibility. This yields key insights into the differences between equilibrium and non-equilibrium behavior in this paradigm model for correlated quantum impurities.
Static spin susceptibility as a function of Teff = V/(1+r)(1+r-1), where r describes the asymmetry of the coupling to the two leads. Curves are for r=1.0 (symmetric coupling), 1.4, 1.8, 2.2, 2.6, 3.0 from bottom to top. The dashed line shows an asymptotically exact result in the limit of vanishing voltage bias.
C. Guo, A. Weichselbaum, S. Kehrein, T. Xiang, and J. von Delft
Using DMRG to Study Quantum Impurity Models with Time-Dependent Hamiltonians
Phys. Rev. B 79, 115137 (2009)
We use the adaptive time-dependent DMRG to study the nonequilibrium dynamics of a quantum system with a time-dependent Hamiltonian. We test the approach using the dissipative Landau-Zener transition as a benchmark and find very good agreement with exact results.
Dissipative Landau-Zener transition for a fast sweep. The black line shows the exact result and the red circles the TD-DMRG algorithm developed in this paper.
A. Hackl and S. Kehrein
Unitary Perturbation Theory Approach to Real-Time Evolution Problems
J. Phys.: Condens. Matter 21, 015601 (2009)
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach builds on the framework of continuous unitary transformations and essentially yields a novel solution method for the Heisenberg equations of motion for an operator. We illustrate the accuracy of this approach by studying dissipative quantum systems on all time scales.
Real time evolution of the spin expectation values starting from a polarized spin in an Ohmic spin-boson model with damping α=0.1 and cutoff ωc=10.0.
M. Möckel and S. Kehrein
Interaction Quench in the Hubbard Model
Phys. Rev. Lett. 100, 175702 (2008)
We investigate the opposite limit of Landau’s Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t = 0. Using the flow equation method, we find three clearly separated time regimes for weak interaction U: i) An initial buildup of correlations where the quasiparticles are formed. ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function. iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.
Figures (a) to (d):
Time evolution of the momentum distribution function for ρU=0.6.
Figure (e): Universal curves for equilibrium and the quasi-steady nonequilibrium state for small U.
A. Hackl and S. Kehrein
Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
Phys. Rev. B 78, 092303 (2008)
We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular
terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.
Monography
Stefan Kehrein
The Flow Equation Approach to Many-Particle Systems
Springer Tracts in Modern Physics Vol. 217
Springer Verlag, 2006
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