Some general laws of statistical physics in the time-dependent Hamiltonian formulation

Through generalized contact transformation methods, broad dynamic relaxation laws (of which those earlier given [1] are mere special cases) are reported and applied to a forced system in contact with a prescribed time-varying reservoir. A new energy law is given.     

Berry phase of many-body system: time-dependent representation method

In this paper, we investigate the Berry phase of many-body system in the time-dependent representation. The formula of Berry phase of many-body system calculating in the time-dependent representation is derived. In this scenario, the Berry phase can be decomposed into two terms, which have different physical meanings respectively. Using these formula, we calculated the Berry phase for the many-spin system coupled by the XXZ exchange interaction. The results show that the Berry phase consists of two contributions which can be interpreted as the flux of a nonquantized monopole and the flux of a Dirac ring respectively.     

Truncation of time-dependent many-body theories

We investigate truncation schemes for the many-body dynamics of finite fermion systems beyond the time-dependent Hartree-Fock (TDHF) approximation. One approach starts from the quantum Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY-)hierarchy of equations of motion for density matrices. It is shown that simple truncation of higher correlations within this scheme is inconsistent because essential exchange correlations are lost. As an alternative, we study the (extended) exp(S) or coupled-cluster formalism. It provides a wider range of applicability. But it also runs into problems with non-unitary propagation after truncation.     

Unifying variational methods for simulating quantum many-body systems

We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks.     

Hamiltonian formulation for the positron trapping model

Summary A Hamiltonian formulation is used to build up an adequate Hamiltonian for the positron trapping model. The number of positrons annihilated in the free state,n _f, or the trapped one,n _v, are considered canonical conjugate variables; this point of view provides a route to propose a Hamiltonian which leads to the previously proposed phenomenological master equations.

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Riassunto Si usa una formulazione hamiltoniana per elaborare un'hamiltoniana adeguata per il modello a trappola dei positroni. Il numero di positroni annichilati nello stato libero,n _f, o in quello intrappolato,n _v, è considerato come variabili coniugate canoniche; in questo senso si fornisce una via per proporre un'hamiltoniana che porti alle equazioni principali fenomenologiche proposte precedentemente.

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Резюме Гамильтонова формулировка используется для конструирования адекватного Гамильтониана для модели захвата позитрона. Число аннигилированных позитронов в свободном состоянии,n _f, или число захваченных позитронов,n _v, рассматриваются как канонически сопряженные переменные. Этот подход приводит к Гамильтониану. Который дает ранее предположенные феноменологические ?управляющие? уравнения.

     

Time-dependent formulation of the linear unitary transformation and the time evolution of general time-dependent quadratic Hamiltonian systems

A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily.     

Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.     

Alternative formulation in the constrained Hamiltonian system of a rigid rotator

An alternative form of the constraint characterizing the motion of a rigid rotator is introduced and is shown to lead to the same constrained Hamiltonian system as the one constructed with the conventional constraintx ²=constant. In this new formulation, the canonical pairs of phase-space variables can easily be found, and the relationx ²=constant appears through an equation of motion rather than through a constraint. Application toO(N) nonlinear sigma model is also discussed.     

On the Kohn variational principles for three-particle systems

The Kohn-type variational principles are formulated, which can be used for calculating the (2 → 3), (3 → 2), and (3 → 3) scattering amplitudes if the two-particle wave functions are known.     

Unconventional Hamilton-type variational principles for electromagnetic elastodynamics

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.     

Functional formulation of dynamical equations for the boson condensate from many-body theory

A functional method applicable to superfluid systems is proposed and the application of the general method to the derivation of equations governing the boson condensate is considered.     

Unconventional Hamilton-type variational principles for analytical mechanics

According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the un-conventional Hamilton-type variational principles of holonomic conservative system in analytical mechanics can be established systematically. This unconventional Hamilton-type variational principle can fully characterize the initial-value problem of analytical mechanics, so that it is an important innovation for the Hamilton-type variational principle. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for analytical mechanics in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work of holonomic conservative system in analytical mechanics, but also to derive systematically the complementary functionals for three-field and two-field unconventional variational principles, and the functional for the one-field one by the generalized Legendre transformation given in this paper. Further, with this new approach, the intrinsic relationship among various principles can be explained clearly. Meanwhile, the unconventional Hamilton-type variational principles of nonholonomic conservative system in analytical mechanics can also be established systematically in this paper.     

Nuclear rotations studied by the time-dependent variational method

A general nuclear rotation including precession and wobbling motion is studied by the time-dependent variational method and a classical equation of motion is derived. The intrinsic wave function associated with the general rotational motion is constructed by making use of the constrained Hartree-Fock method and variables necessary in solving the equation are calculated. The method developed here is applied to a schematic extension of the Nilsson model.     

A variational formulation of relativistic hydrodynamics

We combine Taub's and Ray's variational approaches to relativistic hydrodynamics of perfect fluids into another simple formulation.     

Hamiltonian formulation of Riemann ellipsoid dynamics

A Riemann ellipsoid is a classical fluid with an ellipsoidal boundary whose motion depends linearly on position. The Riemann ellipsoid Newtonian equations of motion are proven to form a Hamiltonian dynamical system. The co-adjoint orbits of a Lie group GCM(3) on which the inertia tensor is positive-definite are the reduced phase spaces of Riemann ellipsoids for which conservation of circulation has been exploited fully.     

Hamiltonian formulation of the anomalous chiral Schwinger model

We construct the hamiltonian formulation of the anomalous chiral Schwinger model, which has recently been shown to yield a consistent unitary theory. The impact of the anomaly on the constraints of the system is exhibited and the system is quantized using an appropriate hamiltonian consistent with the constraints.