相关论文: Paths of zeros of analytic functions describing fi…
(Abbr.) We consider a direct representation of a periodic time-function by means of its zero-crossings. The use of the zero-crossings as the describing parameters is made possible by a singular model of a strongly nonlinear electrical…
An analytic representation with Theta functions on a torus, for systems with variables in Z(d), is considered. Another analytic representation with Theta functions on a strip, for systems with positions in a circle S and momenta in Z, is…
By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which…
We define a zeta function of a finite graph derived from time evolution matrix of quantum walk, and give its determinant expression. Furthermore, we generalize the above result to a periodic graph.
Geometrically, zeroes of a Gaussian analytic function are intersection points of an analytic curve in a Hilbert space with a randomly chosen hyperplane. Mathematical physics provides another interpretation as a gas of interacting particles.…
Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions…
In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
An important quantity in quantum field theory is the vacuum-to-vacuum transition amplitude in the presence of an external source. This quantity is often designated by Z[J] and is the generator for the n-point Greens functions. In textbooks…
We define a zeta function of a graph by using the time evolution matrix of a general coined quantum walk on it, and give a determinant expression for the zeta function of a finite graph. Furthermore, we present a determinant expression for…
It is straightforward to give a sum-over-paths expression for the transition amplitudes of a quantum circuit as long as the gates in the circuit are balanced, where to be balanced is to have all nonzero transition amplitudes of equal…
The R\"ossler System is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of R\"ossler Systems exhibiting a zero-Hopf equilibrium. For R\"ossler Systems near to one of these…
We present a review on the progress in the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
Quantum walks are referred to as quantum analogs to random walks in mathematics. They have been studied as quantum algorithms in quantum information for quantum computers. There are two types of quantum walks. One is the discrete-time…
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential…
In our previous work, we investigated the relation between zeta functions and discrete-time models including random and quantum walks. In this paper, we introduce a zeta function for the continuous-time model (CTM) and consider CTMs…