The second quantization method is applied to classical many-particle systems. Statistical quantities such as free energy and time correlation functions are expressed in terms of creation and annihilation operators. The method is especially useful for the system in which the number of the composite molecules changes with time, e.g. the system including chemical reaction.

We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system and using a high-order finite difference approximation to the kinetic energy operator. We find that our algorithm can simulate η interacting particles using a ...

The second order Sigma-Delta (Σ∆) scheme with linear quantization rule is analyzed for quantizing finite unit-norm tight frame expansions for Rd. Approximation error estimates are derived, and it is shown that for certain choices of frames the quantization error is of order 1/N2, where N is the frame size. However, in contrast to the setting of bandlimited functions there are many situations wh...

math.RT/9808098 This short note is devoted to a second quantization of a classical picture described in [1]. 1.1. Interactive games and intention fields. Definition 1 [1]. An interactive system (with n interactive controls) is a control system with n independent controls coupled with unknown or incompletely known feedbacks (the feedbacks, which are called the behavioral reactions, as well as th...

The second-quantization of a scalar field in an open cavity is formulated, from first principles, in terms of the quasinormal modes (QNMs), which are the eigensolutions of the evolution equation that decay exponentially in time as energy leaks to the outside. This formulation provides a description involving the cavity degrees of freedom only, with the outside acting as a (thermal or driven) so...

Brane-like vertex operators play an important role in a world-sheet formulation of Dbranes and M theory. In this paper we derive the DBI D-brane action from closed NSR string with brane-like states. We also show that these operators carry RR charges and define D-brane wave functions in a second quantized formalism. [email protected] 2 [email protected]

Ah&act-If a point is picked at random inside a regular simplex, octahedron, 600-cell, or other polytope, what is its average squared distance from the centroid? In n-dimensional space, what is the average squared distance of a random point from the closest point of the lattice A, (or D,, , En, A: or D,*)? The answers are given here, together with a description of the Voronoi (or nearest neighbo...

Schwinger terms of current algebra can be identified with nontrivial cyclic cocycles of a Fredholm module. We discuss its temperature dependence. Similar anomalies may occur also in spin systems. In simple examples already an operator–valued cocycle shows up. Lectures given at the XXX–th Karpacz Winter School in Theoretical Physics, Poland, 1994.

i=1 H(ri); (5) HΨ(r1, r2, · · · ) = EΨ(r1, r2, · · · ). (6) (Note: For simplicity, unless necessary, we often write r as r.) Since there is no interaction between particles, the Schrodinger equation is separable. Assume Ψ(r1, r2, · · · , rN ) = φ(r1)φ(r2) · · ·φ(rN ), (7) then Hφαi(ri) = εαiφαi(ri), i = 1, 2, · · ·N. (8) Manybody eigenstate is a product of 1-particle states, Ψα1,α2,···(r1, r2, ...

In this paper, we discuss the classical and quantum mechanics of finite dimensional mechanical systems subject to constraints. We review Dirac’s classical formalism of dealing with such problems and motivate the definition of objects such as singular and non-singular action principles, firstand second-class constraints, and the Dirac bracket. We show how systems with first-class constraints can...