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We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible hamiltonians and corresponding solutions for a finite…
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain…
We prove an analog of Krein's resolvent formula expressing the resolvents of self-adjoint extensions in terms of boundary conditions. Applications to quantum graphs and systems with point interactions are discussed.
The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…
We analyze the role of boundaries in the infrared behavior of quantum field theories. By means of a novel method we calculate the vacuum energy for a massless scalar field confined between two homogeneous parallel plates with the most…
We use the Bethe Ansatz solution for the one dimensional Hubbard model with open boundary conditions and applied boundary fields to study the spectrum of bound states at the boundary. Depending on the strength of the boundary potentials one…
We perform a 1-parameter family of self-adjoint extensions characterized by the parameter $\omega_0$. This allows us to get generic boundary conditions for the quantum oscillator on $N$ dimensional complex projective space($\mathbb{C}P^N$)…
The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this…
For fermionic fields on a compact Riemannian manifold with boundary one has a choice between local and non-local (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied…
The spectral properties of non-self-adjoint extensions $A_{[B]}$ of a symmetric operator in a Hilbert space are studied with the help of ordinary and quasi boundary triples and the corresponding Weyl functions. These extensions are given in…
In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at…
We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…
We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary conditions for the Cahn-Hilliard equation. First we consider…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
The dynamics near the top of a potential barrier is studied in the temperature region where quantum effects become important. The time evolution of the density matrix of a system that deviates initially from equilibrium in the vicinity of…
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…
We consider divergence form operators with complex coefficients on an open subset of Euclidean space. Boundary conditions in the corresponding parabolic problem are dynamical, that is, the time derivative appears on the boundary. As a…
We consider scalar two-dimensional quantum field theories with the factorizing S-matrix which has poles in the physical strip. In our previous work, we introduced the bound state operators and constructed candidate operators for observables…
Invariance in duality transformation, the self-dual property, has important applications in electromagnetic engineering. In the present paper, the problem of most general linear and local boundary conditions with self-dual property is…