Related papers: Two-dimensional delta potential wells and condense…

The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a…

Two-dimensional (2D) materials are a family of layered materials exhibiting rich exotic phenomena, such as valley-contrasting physics. Down to single-particle level, unraveling fundamental physics and potential applications including…

As the fundamental quantum mechanical theory predicts, it is believed that electronic states can be bound only to potential wells and not to potential barriers in any dimension and their energies should be below the background potential.…

A two-dimensional (2D) harmonically trapped interacting Fermi gas is anticipated to exhibit a quantum anomaly and possesses a breathing mode at frequencies different from a classical scale invariant value $\omega_{B}=2\omega_{\perp}$, where…

It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the $O(d)$ symmetry reduction from $d$ degrees of freedom to…

It is shown that a potential consisting of three Dirac's delta functions on the line with disappearing distances can give rise to the discontinuity in wave functions with the proper renormalization of the delta function strength. This can…

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…

The physics of low-energy quasi-particle excitations in disordered d-wave superconductors is a subject of ongoing intensive research. Over the last decade, a variety of conceptually and methodologically different approaches to the problem…

When describing the low-energy physics of bosons in a double-well potential with a high barrier between the wells and sufficiently weak atom-atom interactions, one can to a good approximation ignore the high energy states and thereby obtain…

We present an effective theory describing the low-energy properties of an interacting 2D electron gas at large non-integer filling factors $\nu\gg 1$. Assuming that the interaction is sufficiently weak, $r_s < 1$, we integrate out all the…

The electronic and magnetic properties of many strongly-correlated systems are controlled by a limited number of states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the…

Pair potentials that are bounded at the origin provide an accurate description of the effective interaction for many systems of dissolved soft macromolecules (e.g., flexible dendrimers). Using numerical free-energy calculations, we…

We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be…

Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the…

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent…

We update the constraints on new-physics contributions to Delta F=2 processes from the generalized unitarity triangle analysis, including the most recent experimental developments. Based on these constraints, we derive upper bounds on the…

Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences…

The bound state energies of a 1-dimensional finite quantum square well (FSW) can be determined using a geometric method, involving a smooth mapping between two copies of the complex plane. The method allows one to identify particular…

In this work, a two-dimensional one-band Hubbard model is investigated within a two-pole approximation. The model presents a non-local attractive potential $U (U<0)$ that allows the study of d-wave superconductivity and also includes…

The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…