7,160 research outputs found
Kramers degeneracy theorem in nonrelativistic QED
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is
proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed
total momentum is also investigated.Comment: LaTex, 11 page
Uniqueness of the ground state in the Feshbach renormalization analysis
In the operator theoretic renormalization analysis introduced by Bach,
Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page
Field evolution of the magnetic structures in ErTiO through the critical point
We have measured neutron diffraction patterns in a single crystal sample of
the pyrochlore compound ErTiO in the antiferromagnetic phase
(T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the
[110] direction. We determine all the characteristics of the magnetic structure
throughout the quantum critical point at =2\,T. As a main result, all Er
moments align along the field at and their values reach a minimum. Using
a four-sublattice self-consistent calculation, we show that the evolution of
the magnetic structure and the value of the critical field are rather well
reproduced using the same anisotropic exchange tensor as that accounting for
the local paramagnetic susceptibility. In contrast, an isotropic exchange
tensor does not match the moment variations through the critical point. The
model also accounts semi-quantitatively for other experimental data previously
measured, such as the field dependence of the heat capacity, energy of the
dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
Optical conductivity for a dimer in the Dynamic Hubbard model
The Dynamic Hubbard Model represents the physics of a multi-band Hubbard
model by using a pseudo-spin degree of freedom to dynamically modify the
on-site Coulomb interaction. Here we use a dimer system to obtain analytical
results for this model. The spectral function and the optical conductivity are
calculated analytically for any number of electrons, and the distribution of
optical spectral weight is analyzed in great detail. The impact of polaron-like
effects due to overlaps between pseudo-spin states on the optical spectral
weight distribution is derived analytically. Our conclusions support results
obtained previously with different models and techniques: holes are less mobile
than electrons.Comment: 11 pages, 4 figure
Towards Interpretable Deep Learning Models for Knowledge Tracing
As an important technique for modeling the knowledge states of learners, the
traditional knowledge tracing (KT) models have been widely used to support
intelligent tutoring systems and MOOC platforms. Driven by the fast
advancements of deep learning techniques, deep neural network has been recently
adopted to design new KT models for achieving better prediction performance.
However, the lack of interpretability of these models has painfully impeded
their practical applications, as their outputs and working mechanisms suffer
from the intransparent decision process and complex inner structures. We thus
propose to adopt the post-hoc method to tackle the interpretability issue for
deep learning based knowledge tracing (DLKT) models. Specifically, we focus on
applying the layer-wise relevance propagation (LRP) method to interpret
RNN-based DLKT model by backpropagating the relevance from the model's output
layer to its input layer. The experiment results show the feasibility using the
LRP method for interpreting the DLKT model's predictions, and partially
validate the computed relevance scores from both question level and concept
level. We believe it can be a solid step towards fully interpreting the DLKT
models and promote their practical applications in the education domain
Universal asymptotic behavior in flow equations of dissipative systems
Based on two dissipative models, universal asymptotic behavior of flow
equations for Hamiltonians is found and discussed. Universal asymptotic
behavior only depends on fundamental bath properties but not on initial system
parameters, and the integro-differential equations possess an universal
attractor. The asymptotic flow of the Hamiltonian can be characterized by a
non-local differential equation which only depends on one parameter -
independent of the dissipative system or truncation scheme. Since the fixed
point Hamiltonian is trivial, the physical information is completely
transferred to the transformation of the observables. This yields a more stable
flow which is crucial for the numerical evaluation of correlation functions.
Furthermore, the low energy behavior of correlation functions is determined
analytically. The presented procedure can also be applied if relevant
perturbations are present as is demonstrated by evaluating dynamical
correlation functions for sub-Ohmic environments. It can further be generalized
to other dissipative systems.Comment: 15 pages, 9 figures; to appear in Phys. Rev.
Phase diagrams of the 2D t-t'-U Hubbard model from an extended mean field method
It is well-known from unrestricted Hartree-Fock computations that the 2D
Hubbard model does not have homogeneous mean field states in significant
regions of parameter space away from half filling. This is incompatible with
standard mean field theory. We present a simple extension of the mean field
method that avoids this problem. As in standard mean field theory, we restrict
Hartree-Fock theory to simple translation invariant states describing
antiferromagnetism (AF), ferromagnetism (F) and paramagnetism (P), but we use
an improved method to implement the doping constraint allowing us to detect
when a phase separated state is energetically preferred, e.g. AF and F
coexisting at the same time. We find that such mixed phases occur in
significant parts of the phase diagrams, making them much richer than the ones
from standard mean field theory. Our results for the 2D t-t'-U Hubbard model
demonstrate the importance of band structure effects.Comment: 6 pages, 5 figure
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