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A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…
Perturbation theory in quantum mechanics studies how quantum systems interact with their environmental perturbations. Harmonic perturbation is a rare special case of time-dependent perturbations in which exact analysis exists. Some…
The area law for entanglement provides one of the most important connections between information theory and quantum many-body physics. It is not only related to the universality of quantum phases, but also to efficient numerical simulations…
A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order…
We present a systematic method to expand the quantum complexity of interacting theory in series of coupling constant. The complexity is evaluated by the operator approach in which the transformation matrix between the second quantization…
An approximation method which combines the perturbation theory with the variational calculation is constructed for quantum mechanical problems. Using the anharmonic oscillator and the He atom as examples, we show that the present method…
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…
The effective potential is a widely used phenomenological tool to investigate phase transitions occurring in the early Universe at finite temperature. In the standard perturbative treatment the potential becomes complex in some region of…
A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
In addition to high accuracy, robustness is becoming increasingly important for machine learning models in various applications. Recently, much research has been devoted to improving the model robustness by training with noise…
The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field…
We explore the feasibility of foundation models for the simulation of physical phenomena, with emphasis on continuum (solid and fluid) mechanics. Although so-called learned simulators have shown some success when applied to specific tasks,…
We derive a perturbation theory (PT) for the Lorentz boost operator in the space of two-nucleon wave functions. The latter is expressed in terms of the nucleon-nucleon ($NN$) potentials, developed so far in great detail for their use in the…
We review experiments and theoretical models about the possible mutual interplay between the gravitational field and materials in the superconducting state or other macroscopic quantum states. More generally, we focus on the possibility for…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
In the first part, we investigate the effect of long range particle exchange in ideal bosonic chains. We establish that by using the Heisenberg formalism along with matrix product state representation we can study the evolution as well as…
Under certain conditions we prove the existence of a steady-state transport regime for interacting mesoscopic systems coupled to reservoirs (leads). The partitioning and partition-free scenarios are treated on an equal footing. Our…
We study the entanglement in momentum space of the ground state of a disordered one-dimensional fermion lattice model with attractive interaction. We observe two components in the entanglement spectrum, one of which is related to…