相关论文: Maximum Caliber and quantum physics

Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…

In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in…

Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…

The Lagrangian formalism is used to derive covariant equations that are suitable for use in continuously distributed matter in curved spacetime. Special attention is given to theoretical representation, in which the Lagrangian and its…

Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…

We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the…

In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…

Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical…

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…

We quantize the ModMax oscillator, which is the dimensional reduction of the Modified Maxwell theory to one spacetime dimension. We show that the propagator of the ModMax oscillator satisfies a differential equation related to the Laplace…

In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…

A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…

Variational inequalities are an important mathematical tool for modelling free boundary problems that arise in different application areas. Due to the intricate nonsmooth structure of the resulting models, their analysis and optimization is…

Little is known about the physics frontier of strong acceleration; both classical and quantum physics need further development in order to be able to address this newly accessible area of physics. In this lecture we discuss what strong…

These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…

A gradient-based optimization approach combined with automatic differentiation is employed to ensure high accuracy and scalability when working with high-dimensional parameter spaces. Numerical simulations confirm the effectiveness of the…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…

Quantum optimal control theory is becoming increasingly crucial as quantum devices become more precise, but the need to quickly optimize these systems classically remains a significant bottleneck in their operation. Here we present a new…