相关论文: On Using The Path Integral Formalism to Interpret …
We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…
I discuss the use of path integrals to study strong-interaction physics from first principles. The underlying theory is cast into path integrals which are evaluated numerically using Monte Carlo methods on a space-time lattice. Examples are…
We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
It is shown that classical control diagrams can be mapped one-to-one onto quantum path integrals over measurement amplitudes. To show the practical utility of this method, exact closed-form expressions are derived for the control dynamics…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
The path integral formalism gives a very illustrative and intuitive understanding of quantum mechanics but due to its difficult sum over phases one usually prefers Schr\"odinger's approach. We will show that it is possible to calculate…
There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…
In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, communication channels can be established between them via quantum…
The distribution of entanglement in quantum networks is typically approached under idealized assumptions such as perfect synchronization and centralized control, while classical communication is often neglected. However, these assumptions…
We reformulate Super Quantum Mechanics in the context of integral forms. This framework allows to interpolate between different actions for the same theory, connected by different choices of Picture Changing Operators (PCO). In this way we…
Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However,…