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The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in…
By integrating the pressure equation at the surface of a self coupled curvilinear boundary, one may obtain asymptotic estimates of energy shifts, which is especially useful in lattice QCD studies of nonrelativistic bound states. Energy…
Given a sequence of properly embedded minimal surfaces in a $3$-manifold with local bounds on area and genus, we prove subsequential convergence, smooth away from a discrete set, to a smooth embedded limit surface, possibly with…
In this study, we explore the precise physical quantities in the thermodynamic limit of the one-dimensional Hubbard model with nonparallel boundary magnetic fields based on the off-diagonal Bethe ansatz solution. A particular emphasis is…
By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly…
We study a system of penetrable bosons embedded in a spherical surface. Under the assumption of weak interaction between the particles, the ground state of the system is, to a good approximation, a pure condensate. We employ thermodynamic…
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally, boundary values can appear as additive…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
We analyze the results obtained from a model consisting of the interaction etween the electric quadrupole moment of a moving particle and an electric field. We argue that the system does not support bound states because the motion along the…
This work is intended as an attempt to study the non-perturbative renormalization of bound state problem of finitely many Dirac-delta interactions on Riemannian manifolds, S^2, H^2 and H^3. We formulate the problem in terms of a finite…
We introduce a sum-of-squares SDP hierarchy approximating the ground-state energy from below for quantum many-body problems, with a natural quantum embedding interpretation. We establish the connections between our approach and other…
For the 1D quantum East model with open boundaries, we show that in the limit $s \to -\infty$, the ground state is accurately captured by a simple spin-coherent product state. We further identify a low-entanglement excited eigenstate that…
We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has…
We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the…
We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem…
The scattering of 1D matter wave bright solitons on attractive potentials enables one to populate bound states, a feature impossible with noninteracting wave packets. Compared to noninteracting states, the populated states are renormalized…
We show how changes in unitarity-preserving boundary conditions allow continuous interpolation among the Hilbert spaces of quantum mechanics on topologically distinct manifolds. We present several examples, including a computation of…