Related papers: A Journey Between Two Curves
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
For a given differentiable map $(x,y)\to (X(x,y),Y(x,y))$, which has an inverse, we show that there exists a Hamiltonian flow in which x plays the role of the time variable while y is fixed.
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…
N=1 curve is defined for four dimensional class S theory using Cayley-Hamilton theorem for two commuting matrices. The curve consists of three ingredients: 1: A set of N+1 degree N equations defining a curve; 2: a set of constraints…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
An evolution-type differential equation encodes the intersection theory of tautological classes on the Hilbert scheme of a family of nodal curves.
The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and…
We provide a geometrical interpretation for the series of transformations used by Sakovich to map the third-order nonlinear evolution equation obtained by Chou and Qu to the mKdV equation. We also discuss its bi-Hamiltonian integrability as…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
We consider a two-phase flow of two incompressible, viscous and immiscible fluids which are separated by a sharp interface in the case of a simple phase transition. In this model the interface is no longer material and its evolution is…
We examine \'etale covers of genus two curves that occur in the linear system of a polarizing line bundle of type $(1,d)$ on a complex abelian surface. We give results counting fixed points of involutions on such curves as well as…
A Redfield-like Liouville equation for an open system that couples to one or more leads and exchanges particles with them is derived. The equation is presented for a general case. A case study of time-dependent transport through a single…
Linear evolution equations are considered usually for the time variable being defined on an interval where typically initial conditions or time-periodicity of solutions are required to single out certain solutions. Here we would like to…
We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.
In this paper we establish important relations between Hamiltonian dynamics and Riemannian structures on phase spaces for unitarily evolving finite level quantum systems in mixed states. We show that the energy dispersion (i.e. $1/\hbar$…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
We consider the $H^{-m}$-gradient flow of length for closed plane curves. This flow is a generalization of curve diffusion flow. We investigate the large-time behavior assuming the global existence of the flow. Then we show that the…
We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by $$\mathcal H_N = p_1^2 + p_2^2 +\sum_{n=1}^N \gamma_n(q_1 p_1 + q_2 p_2)^n ,$$ where $q_i$ and $p_i$ are generic canonical variables, $\gamma_n$…