Related papers: Fermionic operatorial model of a system with compe…
We address the nonadiabatic quantum dynamics of macrosystems with several coupled electronic states, taking into account the possibility of multi-state conical intersections. The general situation of an arbitrary number of states and…
We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry,…
A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…
We analyse the discrete-time dynamics of a model of non-interacting fermions coupled to an infinite reservoir formed by a bosonic quantum walk on ${\mathbb Z}$. This dynamics consists of consecutive applications of free evolutions of the…
We propose a model of collective behavior in self-propelled active agents that incorporates a perceptual decision-making process. In this framework, the decision-making dynamics is modeled using quantum formalism. The perceptual decision…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
Artificial agents capable of understanding and aligning with others' intentions are essential for safe and socially robust artificial intelligence. We introduce a computational framework for empathy in active inference agents, grounded in…
Linking the microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: while physical particles are assumed to optimize the global…
In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are…
Simple examples are used to introduce and examine symmetries of open quantum dynamics that can be described by unitary operators. For the Hamiltonian dynamics of an entire closed system, the symmetry takes the expected form which, when the…
A mathematical notion of interaction is introduced for noncommutative dynamical systems, i.e., for one parameter groups of *-automorphisms of $\Cal B(H)$ endowed with a certain causal structure. With any interaction there is a well-defined…
A deterministic system of coupled maps is proposed as a model for economic activity among interacting agents. The values of the maps represent the wealth of the agents. The dynamics of the system is controlled by two parameters. One…
Koopman operator based models emerged as the leading methodology for machine learning of dynamical systems. But their scope is much larger. In fact they present a new take on modeling of physical systems, and even language. In this article…
We derive a model Hamiltonian whose ground state expectation value of any two-body operator coincides with that obtained with the Jastrow correlated wave function of the many-body Fermi system. Using this Hamiltonian we show that the…
In this work, we derive the time-dependent Hartree(-Fock) equations as an effective dynamics for fermionic many-particle systems. Our main results are the first for a quantum mechanical mean-field dynamics for fermions; in previous works,…
We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of…
We have limited our interaction scope to those involving particle-s spin. We then develop operators for handling a many-body treatment of the spin interactions. The results presented show how to promote the particles of the system into the…