Related papers: Compact equations for the envelope theory
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
In an Euclidean $d$-space, the container problem asks to pack $n$ equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\geq 2$ we show that solutions to the container problem can…
A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the $N$-particle Sutherland model, with pair-wise inverse sine-square interactions among the particles,…
It is shown that quantum systems of identical particles can be treated as if they were different when they are in well differentiated states. This simplifying assumption allows the consideration of quantum systems isolated from the rest of…
One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small…
Compactons are solutions of the equations of motion that behave trivially outside a compact region. In general, the operators describing quantum fluctuations above compactons have singularities. However, we show that despite these…
The exact solution of the Schr\"odinger equation for the one-dimensional system of interacting particles with the linear dispersion law in an arbitrary external field is found. The solution is reduced to two groups of particles moving with…
The preparation of highly entangled many-body systems is one of the central challenges of both basic and applied science. The complexity of interparticle interaction and environment coupling increases rapidly with the number of…
Suppose we have identified three clusters of galaxies as being topological copies of the same object. How does this information constrain the possible models for the shape of our Universe? It is shown here that, if the Universe has flat…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…
Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent…
A large collaboration carefully benchmarks 20 first principles many-body electronic structure methods on a test set of 7 transition metal atoms, and their ions and monoxides. Good agreement is attained between the 3 systematically converged…
A Hamiltonian cycle of a graph is a closed path that visits every vertex once and only once. It serves as a model of a compact polymer on a lattice. I study the number of Hamiltonian cycles, or equivalently the entropy of a compact polymer,…
The set of Faddeev and Lippmann--Schwinger integral equations for three-body systems involving Coulomb interactions deduced from a ``three-potential'' picture are shown to be compact for all energies and a method of solution is given.
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
The problem of "what is 'system'?" is in the very foundations of modern quantum mechanics. Here, we point out the interest in this topic in the information-theoretic context. E.g., we point out the possibility to manipulate a pair of…
A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and…
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and…