相关论文: Bound States in n Dimensions (Especially n = 1 and…

In this paper we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to…

Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding…

Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher…

We study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short-range potential in $2+\epsilon $ dimensions. We obtain general expression for the binding energy…

We consider a system of N nonrelativistic bosons in two dimensions, interacting weakly via a short-range attractive potential. We show that for N large, but below some critical value, the properties of the N-boson bound state are universal.…

We study the domain of coupling constants for which a 3-body or 4-body system is bound while none of its subsystems is bound. Limits on the size of the domain are derived from a variant of the Hall--Post inequalities which relate $N$-body…

The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic…

We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.

Some novel TWO-body effects analogous to the well-known THREE-body Efimov effect are predicted. In the systems considered, particle A is constrained on a TRUNCATED or BENT one-dimensional line or two-dimensional plane, or on one side of a…

We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting…

It is well-known that for usual Schroedinger operators weakly coupled bound states exist in dimensions one and two, whereas in higher dimensions the famous Cwikel-Lieb-Rozenblum bound holds. We show for a large class of Schr\"odinger-type…

Nontrivial twisted boundary conditions associated with extra compact dimensions produce an ambiguity in the value of the four dimensional coupling constants of the renormalizable interactions of the twisted fields' zero modes. Resolving…

An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beamsplitter,…

A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition…

It is known that, in an $(m \otimes n)$-dimensional quantum system, the maximum dimension of a subspace that contains only entangled states is (m-1)(n-1). We show that the exact same bound is tight if we require the stronger condition that…

The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same…

We point out that bound states, degenerate in energy but differing in parity, may form in one dimensional quantum systems even if the potential is non-singular in any finite domain. Such potentials are necessarily unbounded from below at…

We investigate the possible existence of the bound state in the system of three bosons interacting with each other via zero-radius potentials in two dimensions (it can be atoms confined in two dimensions or tri-exciton states in…

We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions. The gauge groups we consider are U(N) and SU(N), where N is finite. We formulate the continuum bound state problem in the light-cone formalism, and show that any…

Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N,1) leads to coordinate noncommutativity together with full $N$ dimensional rotation invariance. Through…