1,721,122 research outputs found
Quantum concepts in the social, ecological and biological sciences
No full textQuantum mechanics is traditionally associated with microscopic systems; however, quantum concepts have also been successfully applied to a diverse range of macroscopic systems both within and outside of physics. This book describes how complex systems from a variety of fields can be modelled using quantum mechanical principles; from biology and ecology, to sociology and decision-making. The mathematical basis of these models is covered in detail, furnishing a self-contained and consistent approach. This book provides unique insight into the dynamics of these macroscopic systems and opens new interdisciplinary research frontiers. It will be an essential resource for students and researchers in applied mathematics or theoretical physics who are interested in applying quantum mechanics to dynamical systems in the social, biological or ecological sciences
A Fully Pseudo-Bosonic Swanson Model
Full text linkWe consider a fully pseudo-bosonic Swanson model and we show how its Hamiltonian H can be diagonalized. We also deduce the eigensystem of H†, using the general framework and results deduced in the context of pseudo-bosons. We also construct, using different approaches, the bi-coherent states for the model, study some of their properties, and compare the various constructions
Phase transitions, KMS condition and decision making: an introductory model
No full textWe consider a simple model of interacting agents asked to choose between 'yes' and 'no' to some given question. The agents are described in terms of spin variables, and they interact according to a mean field Heisenberg model. We discuss under which conditions the agents can come out with a common choice. This is made using, in a social context, the notion of KMS states and phase transitions. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'
On non-self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces
No full textIn this paper we discuss some results on non self-adjoint Hamiltonians with real discrete simple
spectrum under the assumption that their eigenvectors form Riesz bases of a certain Hilbert space. Also, we
exhibit a generalization of those results to the case of rigged Hilbert spaces, and we also consider the problem
of the factorization of the aforementioned Hamiltonians in terms of generalized lowering and raising operators
Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics
Full text linkWe propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth
Quantum field inspired model of decision making: Asymptotic stabilization of belief state via interaction with surrounding mental environment
Full text linkThis paper is devoted to justification of the quantum-like model of the process of decision making based on theory of open quantum systems: decision making as decoher- ence. This process is modeled as interaction of a decision maker, Alice, with a mental (information) environment R surrounding her. Such an interaction generates “dissipation of uncertainty” from Alice’s belief-state ρ ( t ) into R and asymptotic stabilization of ρ ( t ) to a steady belief-state. The latter is treated as the decision state. Mathematically the problem under study is about finding constraints on R guaranteeing such stabilization. We found a partial solution of this problem (in the form of sufficient conditions). We present the corresponding decision making analysis for one class of mental environments, so-called “almost homogeneous environments”, with the illustrative examples: a) behavior of electorate interacting with the mass-media “reservoir”; b) consumers’ persuasion. We also comment on other classes of mental environments
On the presence of families of pseudo-bosons in nilpotent Lie algebras of arbitrary corank
Full text linkWe have recently shown that pseudo-bosonic operators realize concrete examples of finite dimensional nilpotent Lie algebras over the complex field. It has been the first time that such operators were analyzed in terms of nilpotent Lie algebras (under prescribed conditions of physical character). On the other hand, the general classification of a finite dimensional nilpotent Lie algebra l may be given via the size of its Schur multiplier involving the so-called corank t(l) of l. We represent l by pseudo-bosonic ladder operators for t(l)≤6 and this allows us to represent l when its dimension is ≤5
On the Pauli group on 2-qubits in dynamical systems with pseudofermions
Full text linkThe group of matrices of Pauli is a finite 2-group of order 16 and
plays a fundamental role in quantum information theory, since it is related to
the quantum information on the 1-qubit. Here we show that both and the
Pauli 2-group of order 64 on 2-qubits, other than in quantum computing,
can also appear in dynamical systems which are described by non self-adjoint
Hamiltonians. This will allow us to represent and in terms of
pseudofermionic operators.Comment: Version of December 2022; 12pp; accepted for publication in Forum
Math. after changes due to the repor
Two-dimensional noncommutative swanson model and its bicoherent states
No full textWe introduce an extended version of the Swanson model, defined on a two-dimensional noncommutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed.We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of L 2 (R 2 )
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