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The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of…
I discuss in this paper the behaviour of the solutions of the so-called q-hyperbolic potentials, i.e. P"oschl-Teller-like and conditionally solvable potentials, in terms of the path integral formalism. The differences in comparison to the…
We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…
We frame the issue of pedestrian dynamics modeling in terms of path-integrals, a formalism originally introduced in quantum mechanics to account for the behavior of quantum particles, later extended to quantum field theories and to…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
In the conformal-gauge two-dimensional quantum gravity, the solution obtained by the perturbative or path-integral approach is compared with the one obtained by the operator-formalism approach. Treatments of the anomaly problem in both…
The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely WKB or instanton calculations. All these methods are…
We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined through a strongly recurrent self-similar local regular Dirichlet…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
A modification of the spiked harmonic oscillator is studied in the case for which the perturbation potential contains both an inverse power and a linear term. It is then possible to evaluate trial functions by solving an integral equation…
The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the…
In this paper, we establish existence of solutions to an indefinite coupled non-linear system. We use partial coercivity to establish existence of a critical point to an indefinite functional and thus the existence of solutions on both…
The solutions of a kind of second-order homogeneous partial differential equation are called (real kernel) alpha-harmonic functions. In this paper, the boundary correspondence and boundary behavior of alpha-harmonic functions are studied,…
In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…
Time evolution of quantum tunneling is studied when the tunneling system is immersed in thermal medium. We analyze in detail the behavior of the system after integrating out the environment. Exact result for the inverted harmonic oscillator…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
In quantum systems with a classical limit, advanced semiclassical methods provide the crucial link between phase-space structures, reflecting the distinction between chaotic, mixed or integrable classical dynamics, and the corresponding…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
The path integral by which quantum field theories are defined is a particular solution of a set of functional differential equations arising from the Schwinger action principle. In fact these equations have a multitude of additional…