Related papers: Particle number projection on a spatial domain
A formalism is presented for analytically obtaining the probability density function, (P_{n}(s)), for the random distance (s) between two random points in an (n)-dimensional spherical object of radius (R). Our formalism allows (P_{n}(s)) to…
We provide a derivation for the particle number densities on phase space for scalar and fermionic fields in terms of Wigner functions. Our expressions satisfy the desired properties: for bosons the particle number is positive, for fermions…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That…
A phase space formulation of the filtering process upon an incident quantum state is developed. This formulation can explain the results of both quantum interference and delayed-choice experiments without making use of the controversial…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering…
We put forward and demonstrate experimentally a {\it quantum-inspired} protocol that allows to quantify the degree of similarity between two spatial shapes embedded in two optical beams without the need to measure the amplitude and phase…
In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed.…
A new formalism is presented for analytically obtaining the probability density function, \( P_{n}(s) \), for the distance between two random points in an \( n \)-dimensional sphere of radius \( R \). Our formalism allows \( P_{n}(s) \) to…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
I discuss the advantages and disadvantages of several procedures, some known and some new, for constructing stationary states within the mean field approximation for a system with pairing correlations and unequal numbers spin-up and…
We consider the statistics of the number of nodal domains aka nodal counts for eigenfunctions of separable wave equations in arbitrary dimension. We give an explicit expression for the limiting distribution of normalised nodal counts and…
Homology has long been accepted as an important computable tool for quantifying complex structures. In many applications, these structures arise as nodal domains of real-valued functions and are therefore amenable only to a numerical study…
In this work, the particle number projection at finite temperature is incorporated into self-consistent Skyrme density functional calculations. In particular, the energies of compound nuclei as a function of deformations are calculated…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
A new stochastic number projection method is proposed. The component of the BCS wave function corresponding to the right number of particles is obtained by means of a Metropolis algorithm in which the weight functions are constructed from…
We develop general formalism of how to relate scattering amplitudes for exclusive processes to spatial image of target hadron. More precisely we show how to determine the spatial distribution of outgoing particles in the space of so-called…
We study the partition-function zeros in mean-field spin-glass models. We show that the replica method is useful to find the locations of zeros in a complex parameter plane. For the random energy model, we obtain the phase diagram in the…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…