Related papers: Virial Theorem for Non-relativistic Quantum Fields…
The spectral theorem is proven for the quantum dynamics of quadratic open systems of n fermions described by the Lindblad equation. Invariant eigenspaces of the many-body Liouvillean dynamics and their largest Jordan blocks are explicitly…
Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a…
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation…
The extreme electromagnetic or gravitational fields associated with some astrophysical objects can give rise to macroscopic effects arising from the physics of the quantum vacuum. Therefore, these objects are incredible laboratories for…
Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…
We study the non-relativistic limit of quantum fields for an inertial and a non-inertial observer. We show that non-relativistic particle states appear as a superposition of relativistic and non-relativistic particles in different frames.…
The Relativistic Mean Field (RMF) approach describing the motion of independent particles in effective meson fields is extended by a microscopic theory of particle vibrational coupling. It leads to an energy dependence of the relativistic…
The virial theorem relates averages of kinetic energy and forces in confined systems. It is widely used to relate stresses in molecular simulation as measured at a boundary and in the interior of a system. In periodic systems, the theorem…
In this paper, we investigate analytic divergence-free vector fields and vector fields admitting a Jacobi multiplier on $n$-dimensional Riemannian manifolds. We first introduce a functional acting on the space of divergence-free vector…
We introduce a weak notion of $2\times 2$-minors of gradients of a suitable subclass of $BV$ functions. In the case of maps in $BV(\mathbb{R}^2;\mathbb{R}^2)$ such a notion extends the standard definition of Jacobian determinant to…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
Vector fields can arise in the cosmological context in different ways, and we discuss both abelian and nonabelian sector. In the abelian sector vector fields of the geometrical origin (from dimensional reduction and Einstein-Eddington…
The symmetry properties of a proposal to go beyond relativistic quantum field theory based on a modification of the commutation relations of fields are identified. Poincar\'e invariance in an auxiliary spacetime is found in the Lagrangian…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
Derrick-type virial identities, obtained via dilatation (scaling) arguments, have a variety of applications in field theories. We deconstruct such virial identities in relativistic gravity showing how they can be recast as self-evident…
It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory…
Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…