Related papers: Rigorous bounds on Transmission, Reflection, and B…
For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant…
In quantum mechanics, the measureable quantities of a given theory are predicted by performing a weighted sum over possibilities. We show how to arrange the possibilities into bundles such that the associated subsums can be viewed as…
Here we aim at justifying rigorously different types of physically relevant diffusive limits for radiative flows. For simplicity, we consider the barotropic situation, and adopt the so-called P1-approximation of the radiative transfer…
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…
We show that there are universal high-temperature relations for transport coefficients of plasmas described by a wide class of field theories with gravity duals. These theories can be viewed as strongly coupled large-Nc conformal field…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
The manifold hypothesis says that natural high-dimensional data lie on or around a low-dimensional manifold. The recent success of statistical and learning-based methods in very high dimensions empirically supports this hypothesis,…
We discuss the relationship between the Bogoliubov transformations, squeezed states, entanglement and maximum violation of the Bell-CHSH inequality. In particular, we point out that the construction of the four bounded operators entering…
Chernoff bounds are a powerful application of the Markov inequality to produce strong bounds on the tails of probability distributions. They are often used to bound the tail probabilities of sums of Poisson trials, or in regression to…
We explore the influence of turbulence on the transport of energetic particles by using test-particle simulations. We compute parallel and perpendicular diffusion coefficients for two-component turbulence, isotropic turbulence, a model…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…
The Bohm interpretation of quantum mechanics is applied to a transmission and reflection process in a double potential well. We consider a time dependent periodic wave function and study the particle trajectories. The average time,…
The transport properties of certain strongly coupled thermal gauge theories can be determined from their effective description in terms of gravity or superstring theory duals. Here we provide a short summary of the results for the shear and…
Effective Lifshitz black holes with arbitrary dynamical exponent are addressed in the fluid/gravity membrane paradigm. The transport and the response coefficients in the dual Lifshitz field theory are calculated and analyzed, including the…
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…
The commonly used quasilinear approximation allows one to calculate the turbulent transport coefficients for the mean of a passive scalar or a magnetic field in a given velocity field. Formally, the quasilinear approximation is exact when…
This short essay discusses the application of Bogoliubov's theory of superfluidity in the context of quantum phase transitions.
Phase-space procedure based on coherent state representation is proposed for investigation of reflection and transmission of light beams at a curved dielectric boundary. Numerical simulations of reflection and transmission of light at…
We focus on the (sharp) threshold phenomena arising in some reaction-diffusion equations supplemented with some compactly supported initial data. In the so-called ignition and bistable cases, we prove the first sharp quantitative estimate…
It was recently shown that a generalization of quantum Turing machines (QTMs), in which potentials are associated with elementary steps or transitions of the computation, generates potential distributions along computation paths of states…