91 research outputs found
Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems
It is one of the most important and long-standing issues of physics to derive
the irreversibility out of a time-reversal symmetric equation of motion. The
present paper considers the breaking of the time-reversal symmetry in open
quantum systems and the emergence of an arrow of time. We claim that the
time-reversal symmetric Schr\"{o}dinger equation can have eigenstates that
break the time-reversal symmetry if the system is open in the sense that it has
at least a countably infinite number of states. Such eigenstates, namely the
resonant and anti-resonant states, have complex eigenvalues. We show that,
although these states are often called "unphysical," they observe the
probability conservation in a particular way. We also comment that the
seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the
resonant and anti-resonant states, and hence there is no contradiction in the
fact that it has complex eigenvalues. We finally show how the existence of the
states that break the time-reversal symmetry affects the quantum dynamics. The
dynamics that starts from a time-reversal symmetric initial state is dominated
by the resonant states for ; this explains the phenomenon of the arrow of
time, in which the decay excels the growth. The time-reversal symmetry holds in
that the dynamics ending at a time-reversal symmetric final state is dominated
by the anti-resonant states for .Comment: 14 pages, 4 figures, published in Entropy Journal Special Issue
"Coherence in Open Quantum Systems
Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula
We study the electron transport in open quantum-dot systems described by the
interacting resonant-level models with Coulomb interactions. We consider the
situation in which the quantum dot is connected to the left and right leads
asymmetrically. We exactly construct many-electron scattering eigenstates for
the two-lead system, where two-body bound states appear as a consequence of
one-body resonances and the Coulomb interactions. By using an extension of the
Landauer formula, we calculate the average electric current for the system
under bias voltages in the first order of the interaction parameters. Through a
renormalization-group technique, we arrive at the universal electric current,
where we observe the suppression of the electric current for large bias
voltages, i.e., negative differential conductance. We find that the suppressed
electric current is restored by the asymmetry of the system parameters.Comment: 27 pages, 3 figure
Tunable Bound States in Continuum by Optical Frequency
We demonstrate the existence of tunable bound-states in continuum (BIC) in a
1-dimensional quantum wire with two impurities induced by an intense
monochromatic radiation field. We found that there is a new type of BIC due to
the Fano interference between two optical transition channels, in addition to
the ordinary BIC due to a geometrical interference between electron wave
functions emitted by impurities. In both cases the BIC can be achieved by
tuning the frequency of the radiation field.Comment: 5 figure
Wave function propagation in a two-dimensional paramagnetic semiconductor from an impurity
We simulated modifications to a model of a two-dimensional paramagnetic
semiconductor called the half-BHZ model, also known as the QWZ model, and
simulated a modified full BHZ model, where a time reversal pair is introduced.
Our modifications to the models include adding single and multiple impurities
connected to the lattices or as a connection between the time-reversal pairs.
We employed the Julia programming language to show how to speed up calculations
for time evolutions. By simulating the time evolutions, we could observe the
differences in the effects of these modifications. Our simulations showed the
presence of scattering behavior associated with the infinite QWZ model
topological states. Moreover, we observed scattering and absorption behavior
related to the parameters and placements of impurities and Hamiltonian
imaginary component's symmetry or anti-symmetry. These tools and early results
lay the foundations for developing electronic devices that use the models'
unique scattering and absorption behaviors and explore more complex and
physically accurate modifications to the models
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