Related papers: Quasilocal Conservation Laws in the Quantum Hirota…
In the present paper, we study quantum Sobolev spaces whose elements are operators of the Hilbert-Schmidt class. We construct these Sobolev spaces from the Fourier transform for operators. Next, we obtain continuous embedding theorems.…
A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted…
We propose that probability in quantum theory, like energy in general relativity, acquires a fundamentally quasilocal character in curved spacetime. Interpreting Hermiticity as the symmetry associated with inner-product conservation, we…
On the basis of (i) the discrete and continuous symmetries (and corresponding conserved charges), (ii) the ensuing algebraic structures of the symmetry operators and conserved charges, and (iii) a few basic concepts behind the subject of…
We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We do so by introducing a family of one-dimensional local quantum rotor and bosonic models which conserve finite Fourier…
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The…
We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided…
Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can…
In non-diffusive conduction regimes of strongly correlated quantum electron systems, electromagnetic perturbations simultaneously probe the electronic dynamics in time and space: the exchanged energy $\hbar \omega$ excites retarded, i.e.,…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
A major challenge to the control of infinite dimensional quantum systems is the irreversibility which is often present in the system dynamics. Here we consider systems with discrete-spectrum Hamiltonians operating over a Schwartz space…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
The hamiltonian formalism is developed for the sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of…
We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are…
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…
We classify zeroth-order conservation laws of systems from the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The classification is carried out…
In this paper, we introduce the concept of completely linear degeneracy for quasilinear hyperbolic systems in several space variables, and then get an interesting property for multidimensional hyperbolic conservation laws. Some examples and…
Quantum non-linear SCHROEDINGER equation is equivalent to Lieb-Liniger model. It has non-trivial conservation laws. Recently these conservation laws were used for evaluation of the three-body recombination rate for interacting gas of…
In the Kogut-Susskind formulation of lattice gauge theories, a set of quantum numbers resides at the ends of each link to characterize the vertex-local gauge field. We discuss the role of these quantum numbers in propagating correlations…
We derive and implement symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations and apply them to the molecular electronic structure problem. All symmetries (particle number, spin, spatial, and complex conjugation) are deliberately…