scholarly journals Population model of Temnothorax albipennis as a distributed dynamical system II: secret of "chemical reaction" in collective house-hunting in ant colonies is unveiled by operator methods

2021 ◽  
Author(s):  
Siwei Qiu
Keyword(s):  
Master Equation ◽  
Evolution Operator ◽  
Fock Space ◽  
Equations Of Motion ◽  
Functional Space ◽  
Functional Integral ◽  
Death Process ◽  
Number Representation ◽  
Many Body ◽  
Field Equations

The collective intelligence of animal groups is a complex algorithm for computer scientist and a many-body problem for physics of living system. We show how the time evolution of features in such a system, like number of ants in particular state for colonies, can be mapped to many-body problems in non-equilibrium statistical mechanics. There exist role transitions of active and passive ant between distributed functions, including exploration, assessing, recruiting and transportation in the house-hunting process. Theoretically, such a process can be approximately described as birth-death process where large number of particles living in the Fock space and particles of one sub-type transfer to a different sub-type with some probability. Started from the master equation with constrain of the quorum criterion, we express the evolution operator as a functional integral mapping from operators acting on Fock space in number representation to functional space in coherent state representation. We then read out the action from the evolution operator, and we use least action principal equations of motion, which are the number field equations. The equations we get are couple ordinary differential equations, which can faithfully describe the original master equation, and hence fully describe the system. This method provides us differential equation-based algorithm, which allow us explore parameter space with respect to more complicated agent-based algorithm. The algorithm also allows exploring stochastic process with memory in a Markovian way, which provide testable prediction on collective decision making.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

A Derivation of Relativistically-Invariant Nonlinear Field Equations for Strongly Interacting Many-Body Systems

1997 ◽  
Vol 11 (07) ◽  
pp. 929-944 ◽  
Author(s):  
J. A. Tuszyński ◽  
J. M. Dixon
Keyword(s):  
Field Equation ◽  
Equations Of Motion ◽  
Nonlinear Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Relativistic Regime ◽  
Klein Gordon ◽  
Many Body Systems ◽  
Nonlinear Field Equations

We re-examine the derivation of nonlinear field equations for a system of strongly interacting quasiparticles. Emphasis is placed on typical dispersion relations in the relativistic regime. Through Heisenberg's equations of motion for second-quantised operators we demonstrate that interacting many-body systems are described by a nonlinear Klein–Gordon type field equation. Its nonrelativistic equivalent was previously shown to be of the nonlinear Schrödinger type.

On a non-symmetric theory of the pure gravitational field

1958 ◽  
Vol 54 (1) ◽  
pp. 72-80 ◽  
Author(s):  
D. W. Sciama
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Symmetric Tensor ◽  
Momentum Tensor ◽  
Unified Field Theory ◽  
Field Equations ◽  
Metric Tensor ◽  
Unified Field

ABSTRACTIt is suggested, on heuristic grounds, that the energy-momentum tensor of a material field with non-zero spin and non-zero rest-mass should be non-symmetric. The usual relationship between energy-momentum tensor and gravitational potential then implies that the latter should also be a non-symmetric tensor. This suggestion has nothing to do with unified field theory; it is concerned with the pure gravitational field.A theory of gravitation based on a non-symmetric potential is developed. Field equations are derived, and a study is made of Rosenfeld identities, Bianchi identities, angular momentum and the equations of motion of test particles. These latter equations represent the geodesics of a Riemannian space whose contravariant metric tensor is gij–, in agreement with a result of Lichnerowicz(9) on the bicharacteristics of the Einstein–Schrödinger field equations.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

scholarly journals Generalized Master Equation Approach to Time-Dependent Many-Body Transport

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 731 ◽  
Author(s):  
Moldoveanu ◽  
Manolescu ◽  
Gudmundsson
Keyword(s):  
Master Equation ◽  
Single Mode ◽  
Continuous Model ◽  
Coupled Systems ◽  
Many Body ◽  
Technical Problems ◽  
Transient Transport ◽  
Formal Framework ◽  
Master Equation Approach ◽  
Generalized Master Equation

We recall theoretical studies on transient transport through interacting mesoscopic systems.It is shown that a generalized master equation (GME) written and solved in terms of many-body statesprovides the suitable formal framework to capture both the effects of the Coulomb interaction andelectron–photon coupling due to a surrounding single-mode cavity. We outline the derivation of thisequation within the Nakajima–Zwanzig formalism and point out technical problems related to itsnumerical implementation for more realistic systems which can neither be described by non-interactingtwo-level models nor by a steady-stateMarkov–Lindblad equation. We first solve the GME for a latticemodel and discuss the dynamics of many-body states in a two-dimensional nanowire, the dynamicalonset of the current-current correlations in electrostatically coupled parallel quantum dots and transientthermoelectric properties. Secondly, we rely on a continuous model to get the Rabi oscillations ofthe photocurrent through a double-dot etched in a nanowire and embedded in a quantum cavity.A many-bodyMarkovian version of the GME for cavity-coupled systems is also presented.

scholarly journals Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

2019 ◽  
Vol 100 (21) ◽  
Author(s):  
Giuseppe De Tomasi ◽  
Daniel Hetterich ◽  
Pablo Sala ◽  
Frank Pollmann
Keyword(s):  
Fock Space ◽  
Many Body ◽  
Strongly Interacting ◽  
Interacting Systems

Feldtheoretische Konstruktion der Jordan—Brans—Dicke-Theorie / Fieldtheoretic Construction of the Jordan-Brans-Dicke-Theory

1971 ◽  
Vol 26 (4) ◽  
pp. 599-622
Author(s):  
H. von Grünberg
Keyword(s):  
Gauge Group ◽  
Tensor Field ◽  
Mathematical Proof ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Flat Space ◽  
Momentum Tensor ◽  
Field Equations ◽  
Tensor Theory ◽  
Generally Covariant

Abstract In the framework of Lorentz invariant theories of gravitation the fieldtheoretic approach of the generally covariant Jordan-Brans-Dicke-theory is investigated.It is shown that a slight restriction of the gauge group of Einstein's linear tensor theory leads to the linearized Jordan-Brans-Dicke-theory. The problem of the inconsistency of the field equations and the equations of motion is solved by introducing the Landau-Lifschitz energy momentum tensor of the gravitational field as an additional source term into the field equations. The second order of the theory together with the corresponding gauge group are calculated explicitly. By means of the structure of the gauge group of the tensor field it is possible to identify the successive orders of the scalar-tensor theory as an expansion of the Jordan-Brans-Dicke-theory in flat space-time. The question of the uniqueness of the procedure is answered by showing that the structure of the gauge group of the tensor field is predetermined by the linear equations of motion. The mathematical proof of this fact confirms formally the meaning of the equations of motion for the geometry of space.

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