9 research outputs found
Correlations and enlarged superconducting phase of - chains of ultracold molecules on optical lattices
We compute physical properties across the phase diagram of the -
chain with long-range dipolar interactions, which describe ultracold polar
molecules on optical lattices. Our results obtained by the density-matrix
renormalization group (DMRG) indicate that superconductivity is enhanced when
the Ising component of the spin-spin interaction and the charge component
are tuned to zero, and even further by the long-range dipolar interactions.
At low densities, a substantially larger spin gap is obtained. We provide
evidence that long-range interactions lead to algebraically decaying
correlation functions despite the presence of a gap. Although this has recently
been observed in other long-range interacting spin and fermion models, the
correlations in our case have the peculiar property of having a small and
continuously varying exponent. We construct simple analytic models and
arguments to understand the most salient features.Comment: published version with minor modification
Functional renormalization group for non-equilibrium quantum many-body problems
We extend the concept of the functional renormalization for quantum many-body
problems to non-equilibrium situations. Using a suitable generating functional
based on the Keldysh approach, we derive a system of coupled differential
equations for the -particle vertex functions. The approach is completely
general and allows calculations for both stationary and time-dependent
situations. As a specific example we study the stationary state transport
through a quantum dot with local Coulomb correlations at finite bias voltage
employing two different truncation schemes for the infinite hierarchy of
equations arising in the functional renormalization group scheme
Time-dependent DMRG Study on Quantum Dot under a Finite Bias Voltage
Resonant tunneling through quantum dot under a finite bias voltage at zero
temperature is investigated by using the adaptive time-dependent density matrix
renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson
Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the
ground state wave function is calculated with the usual DMRG method. Then the
time evolution of the wave function due to the slowly changing bias voltage
between the two leads is calculated by using the TdDMRG technique. Even though
the system size is finite, the expectation values of current operator show
steady-like behavior for a finite time interval, in which the system is
expected to resemble the real nonequilibrium steady state of the infinitely
long system. We show that from the time intervals one can obtain quantitatively
correct results for differential conductance in a wide range of bias voltage.
Finally we observe an anomalous behavior in the expectation value of the double
occupation operator at the dot as a function of
bias voltage
Far-from-equilibrium quantum many-body dynamics
The theory of real-time quantum many-body dynamics as put forward in Ref.
[arXiv:0710.4627] is evaluated in detail. The formulation is based on a
generating functional of correlation functions where the Keldysh contour is
closed at a given time. Extending the Keldysh contour from this time to a later
time leads to a dynamic flow of the generating functional. This flow describes
the dynamics of the system and has an explicit causal structure. In the present
work it is evaluated within a vertex expansion of the effective action leading
to time evolution equations for Green functions. These equations are applicable
for strongly interacting systems as well as for studying the late-time
behaviour of nonequilibrium time evolution. For the specific case of a bosonic
N-component phi^4 theory with contact interactions an s-channel truncation is
identified to yield equations identical to those derived from the 2PI effective
action in next-to-leading order of a 1/N expansion. The presented approach
allows to directly obtain non-perturbative dynamic equations beyond the widely
used 2PI approximations.Comment: 20 pp., 6 figs; submitted version with added references and typos
corrected
Characteristic points and cycles in planar kinematics with application to the human gait
Purpose: We present a novel method to process kinematical data typically coming from measurements of joints. This method will be illustrated through two examples. Methods: We adopt theoretical kinematics together with the principle of least action. We use motion and inverse motion for describing the whole experimental situation theoretically. Results: By using the principle of least action, the data contain information about inherent reference points, which we call characteristic points. These points are unique for direct and inverse motion. They may be viewed as centers of the fixed and moving reference systems. The respective actions of these characteristic points are analytically calculated. The sum of these actions defines the kinematical action. This sum is by design independent of the choice of reference system. The minimality of the kinematical action can be used again to select numerically one representative cycle in empirically given, approximately periodic motions. Finally, we illustrate the theoretical approach making use of two examples worked out, hinge movement and the sagittal component of the movement of a human leg during gait. Conclusions: This approach enables automatic cycle choices for evaluating large databases in order to compare and to distinguish empirically given movements. The procedure can be extended to three dimensional movements
The description of the human knee as four-bar linkage
Purpose: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nägerl which is applicable under form closure. Methods: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. Results: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. Conclusions: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee