92 research outputs found
Kadanoff-Baym equations for interacting systems with dissipative Lindbladian dynamics
The extraordinary quantum properties of nonequilibrium systems governed by
dissipative dynamics have become a focal point in contemporary scientific
inquiry. The Nonequilibrium Green's Functions (NEGF) theory provides a
versatile method for addressing driven {\em non-dissipative} systems, utilizing
the powerful diagrammatic technique to incorporate correlation effects. We here
present a second-quantization approach to the {\em dissipative} NEGF theory,
reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending
the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation
theory for many-body Lindblad operators, the formalism enables correlated and
dissipative real-time simulations for the exploration of transient and
steady-state changes in the electronic, transport, and optical properties of
materials.Comment: 10 page
Nonadiabatic Van der Pol oscillations in molecular transport
The force exerted by the electrons on the nuclei of a current-carrying
molecular junction can be manipulated to engineer nanoscale mechanical systems.
In the adiabatic regime a peculiarity of these forces is negative friction,
responsible for Van der Pol oscillations of the nuclear coordinates. In this
work we study the robustness of the Van der Pol oscillations against
high-frequency bias and gate voltage. For this purpose we go beyond the
adiabatic approximation and perform full Ehrenfest dynamics simulations. The
numerical scheme implements a mixed quantum-classical algorithm for open
systems and is capable to deal with arbitrary time-dependent driving fields. We
find that the Van der Pol oscillations are extremely stable. The nonadiabatic
electron dynamics distorts the trajectory in the momentum-coordinate phase
space but preserves the limit cycles in an average sense. We further show that
high-frequency fields change both the oscillation amplitudes and the average
nuclear positions. By switching the fields off at different times one obtains
cycles of different amplitudes which attain the limit cycle only after
considerably long times.Comment: 12 pages, 7 figure
On-Site Repulsion as the Source of Pairing in Carbon Nanotubes and Intercalated Graphite
We show that different non-conventional superconductors have one fundamental
feature in common: pair eigenstates of the Hamiltonian are repulsion-free, the
W=0 pairs. In extended Hubbard models, pairing can occur for resonable
parameter values. For nanotubes the binding energy of the pair depends
strongly on the filling and decreases towards a reduced but nonzero value for
the graphite sheet .Comment: 4 pages, 2 figure
Pairing in the Hubbard model: the Cu_{5}O_{4} Cluster versus the Cu-O plane
We study the Cu_{5}O_{4} cluster by exact diagonalization of a three-band
Hubbard model and show that bound electron or hole pairs are obtained at
appropriate fillings, and produce superconducting flux quantisation.
The results extend earlier cluster studies and illustrate a canonical
transformation approach to pairing that we have developed recently for the full
plane. The quasiparticles that in the many-body problem behave like Cooper
pairs are W=0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian
with vanishing on-site repulsion. The cluster allows W=0 pairs of d symmetry,
due to a spin fluctuation, and s symmetry, due to a charge fluctuation. Flux
quantisation is shown to be a manifestation of symmetry properties that hold
for clusters of arbitrary size.Comment: 13 pages, 3 figures, a few intermediate steps added for clarit
Magnetic moments in biased quantum circuits
We consider a quantum ring connected to leads and the current which is excited by biasing the circuit in the absence of external magnetic field. The magnetic moment Mring that arises in this way depends on the current distribution inside the ring. We perform a thought experiment in which Mring is determined by measuring the torque due to an infinitesimally small probe magnetic field. This leads to a definition Mring, which is given by the derivative of the grand-canonical energy of the quantum ring with respect to an external magnetic flux in the zero flux limit. We develop the many-body formalism by Green's-function techniques and carry on illustrative model calculations. The resulting theory predicts that at small bias the current in the ring is always laminar, that is, the magnetic moment vanishes in linear-response theory. The approach most naturally lends itself to include induction effects by a self-consistent procedure
Symmetric Hubbard Systems with Superconducting Magnetic Response
In purely repulsive, -symmetric Hubbard clusters a correlation effect
produces an effective two-body attraction and pairing; the key ingredient is
the availability of W=0 pairs, that is, two-body solutions of appropriate
symmetry. We study the tunneling of bound pairs in rings of 5-site units
connected by weak intercell links; each unit has the topology of a CuO
cluster and a repulsive interaction is included on every site. Further, we test
the superconducting nature of the response of this model to a threading
magnetic field. We present a detailed numerical study of the two-unit ring
filled with 6 particles and the three-unit ring with 8 particles; in both cases
a lower filling yields normal behavior. In previous studies on 1d Hubbard
chains, level crossings were reported (half-integer or fractional Aharonov-Bohm
effect) which however cannot be due to superconducting pairs. In contrast, the
nontrivial basis of clusters carrying W=0 pairs leads to genuine
Superconducting Flux Quantization (SFQ). The data are understood in terms of a
cell-perturbation theory scheme which is very accurate for weak links. This
low-energy approach leads to an effective hard core boson Hamiltonian which
naturally describes itinerant pairs and SFQ in mesoscopic rings. For the
numerical calculations, we take advantage of a recently proposed exact
diagonalization technique which can be generally applied to many-fermion
problems and drastically reduces the size of the matrices to be handled.Comment: 12 pages, 11 figure
An ab-initio approach to describe coherent and non-coherent exciton dynamics
The use of ultra-short laser pulses to pump and probe materials activates a
wealth of processes which involve the coherent and non coherent dynamics of
interacting electrons out of equilibrium. Non equilibrium (NEQ) many body
perturbation theory (MBPT) offers an equation of motion for the density-matrix
of the system which well describes both coherent and non coherent processes. In
the non correlated case there is a clear relation between these two regimes and
the matrix elements of the density-matrix. The same is not true for the
correlated case, where the potential binding of electrons and holes in
excitonic states need to be considered. In the present work we discuss how
NEQ-MBPT can be used to describe the dynamics of both coherent and non-coherent
excitons in the low density regime. The approach presented is well suited for
an ab initio implementation
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