Related papers: The Spectral Shift Function and The Friedel Sum Ru…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
In this paper, the translational addition theorem for spherical functions is employed to exactly calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere suspended in an inviscid fluid. The radiation force is…
Near the critical temperature of the chiral phase transition, a collective excitation due to fluctuation of the chiral order parameter appears. We investigate how it affects the quark spectrum near but above the critical temperature. The…
For a system with a fixed number of electrons, the total optical sum is a constant, independent of many-body interactions, of impurity scattering and of temperature. For a single band in a metal, such a sum rule is no longer independent of…
The scattering cross section of the resonant inelastic light scattering is represented as a correlation function in the Keldysh-Schwinger functional integral formalism. The functional integral approach enables us to compute the cross…
Recently developed time-independent bound-state perturbation theory is extended to treat the scattering domain. The changes in the partial wave phase shifts are derived explicitly and the results are compared with those of other methods.
The frequency shift of spectral lines from astronomical objects is most often explained by the Doppler Effect arising in relative motion and the broadening of a particular line is supposed to depend on the absolute temperature, pressure or…
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
It is reviewed how Compton scattering sum rules relate low-energy nucleon structure quantities to the nucleon excitation spectrum. In particular, the GDH sum rule and recently proposed extensions of it will be discussed. These extensions…
Spectral functions, such as the zeta functions, are widely used in Quantum Field Theory to calculate physical quantities. In this work, we compute the electrostatic potential and field due to an infinite discrete distribution of point…
We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic…
In this paper, we determine the almost sure multifractal spectrum of a class of random functions constructed as sums of pulses with random dilations and translations. In addition, the continuity modulii of these functions is investigated.
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in…
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…
A family of threshold parameters which probe the stability of chiral predictions is considered. The relevant criteria for the choice of threshold parameters are discussed. Sum rules for these quantities are derived from dispersion relations…