Single Bound State Research Articles

Impact of Side-Chain Hydrophilicity on Packing, Swelling, and Ion Interactions in Oxy-Bithiophene Semiconductors.

Exchanging hydrophobic alkyl-based side chains to hydrophilic glycol-based side chains is a widely adopted method for improving mixed-transport device performance, despite the impact on solid-state packing and polymer-electrolyte interactions being poorly understood. Presented here is a molecular dynamics (MD) force field for modeling alkoxylated and glycolated polythiophenes. The force field is validated against known packing motifs for their monomer crystals. MD simulations, coupled with X-ray diffraction (XRD), show that alkoxylated polythiophenes will pack with a "tilted stack" and straight interdigitating side chains, whilst their glycolated counterpart will pack with a "deflected stack" and an s-bend side-chain configuration. MD simulations reveal water penetration pathways into the alkoxylated and glycolated crystals-through the π-stack and through the lamellar stack respectively. Finally, the two distinct ways triethylene glycol polymers can bind to cations are revealed, showing the formation of a metastable single bound state, or an energetically deep double bound state, both with a strong side-chain length dependence. The minimum energy pathways for the formation of the chelates are identified, showing the physical process through which cations can bind to one or two side chains of a glycolated polythiophene, with consequences for ion transport in bithiophene semiconductors.

Formation of bound states from the edge states of 2D topological insulator by macroscopic magnetic barriers

A model of bound state formation from the delocalized edge states of 2D topological insulator (TI) is derived by considering the effects of magnetic barriers attached to the edge of the HgTe/CdTe quantum well. The resulting structure has a spatial form of 1D quantum dot (QD) with variable number of bound states depending on barrier parameters. The spatial profile of exchange interaction between the edge states and barriers is derived from the interaction with single impurity magnetic moment and is generalized for the barrier bulk structure formed by ensemble of impurities. The resulting Hamiltonian is studied as a function of barrier parameters including their strength and orientation of the magnetic moments. It is shown that for parallel magnetization of two barriers at least two discrete levels are formed regardless of the barrier strength. For antiparallel magnetization at least a single bound state is formed for any strength of the barriers. Our results may help in design of novel types of QDs based on TIs.

Fractional nonlinear surface impurity in a 2D lattice

We study the formation of localized modes around a generalized nonlinear impurity which is located at the boundary of a semi-infinite square lattice, and where we replace the standard discrete Laplacian by a fractional one, characterized by a fractional exponent 0<α<1 where α=1 marks the standard, non-fractional case. We specialize to two impurity cases: impurity at an “edge” and impurity at a “corner” and use the formalism of lattice Green functions to obtain in closed form the bound state energy and its mode amplitude. It is found that, for any fractional exponent and for impurity strengths above a certain threshold, there is always a single bound state for the linear impurity, while for the nonlinear (cubic) case, up to two bound states are possible. At small fractional exponents, the energy of the impurity mode becomes directly proportional to the impurity strength.

The fractional nonlinear impurity: A Green function approach

We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies and the mode profiles are computed in closed form, for different fractional exponents and different impurity strengths. The energies of the impurity mode lie outside the linear band whose bandwidth decreases steadily as the fractional exponent decreases. For any fractional exponent values, there is always a single bound state for the linear impurity while for the nonlinear (Kerr) case, up to two bound states are possible, for impurity strengths above certain threshold. The energy of the linear mode (or that of the upper energy nonlinear one), becomes directly proportional to the impurity strength at large impurity strengths. The transmission of plane waves is also computed in closed form for several fractional exponents, and various impurity strengths. We observe that fractionality tends to increase the overall transmission. The selftrapping transition for the nonlinear impurity shifts to lower nonlinearity values as the fractional exponent is decreased. In both cases, linear and nonlinear, we observe a form of trapping at zero impurity strength, which can be explained by the near-degeneracy of the spectrum in the limit of a small fractional exponent.

Correlated nature of hybrid s -wave superconducting and Rashba lattices

We elucidate the electronic state of a two-dimensional (2D) Rashba square lattice proximitized to a square monolayer $s$-wave superconductor, analyzing the role played by dynamical electron-electron interactions. The $\text{2D}+\text{2D}$ proximity effect induces sharp Bogoliubov and low-energy Andreev-reflected bound states, suppressing the $s$-wave gap globally. Dynamical correlations strongly renormalize the Bogoliubov quasiparticles and the Andreev levels, evolving the spin-resolved Andreev linewidths into a single bound state. We explore the channel- and spin-resolved spectral functions and analyze the reconstructed superconducting state, showing that the Rashba spin-orbit coupling drives strong channel differentiation. The mutual interplay between electron-electron and spin-orbit interactions, with proximity-induced electron pairing, lead us to introduce a generally applicable mechanism for designing Majorana fermions in 2D superconducting structures.

Geometric effects on the electronic structure of curved nanotubes and curved graphene: the case of the helix, catenary, helicoid, and catenoid

Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative description of the conduction electrons' behavior. The confinement process of a quantum particle to a curve or surface leads us, in the so-called "confining potential formalism" (CPF), to a geometry-induced potential (GIP) in the effective Schr\"odinger equation. With these considerations, this work aims to study in detail the consequences of constraining a quantum particle to a helix, catenary, helicoid, or catenoid, exploring the relations between these curves and surfaces using differential geometry. Initially, we use the variational method to estimate the energy of the particle in its ground state, and thus, we obtain better approximations with the use of the confluent Heun function through numerical calculations. Thus, we conclude that a quantum particle constrained to an infinite helix has its angular momentum quantized due to the geometry of the curve, while in the cases of the catenary, helicoid, and catenoid the particle can be found either in a single bound state or in excited states which constitute a continuous energy band. Additionally, we propose measurements of physical observables capable of discriminating the topologies of the studied surfaces, in the context of topological metrology.

Trapped fractional charges at bulk defects in topological insulators.

Topological crystalline insulators (TCIs) can exhibit unusual, quantized electric phenomena such as fractional electric polarization and boundary-localized fractional charge1-6. This quantized fractional charge is the generic observable for identification of TCIs that lack clear spectral features5-7, including ones with higher-order topology8-11. It has been predicted that fractional charges can also manifest where crystallographic defects disrupt the lattice structure of TCIs, potentially providing a bulk probe of crystalline topology10,12-14. However, this capability has not yet been confirmed in experiments, given that measurements of charge distributions in TCIs have not been accessible until recently11. Here we experimentally demonstrate that disclination defects can robustly trap fractional charges in TCI metamaterials, and show that this trapped charge can indicate non-trivial, higher-order crystalline topology even in the absence of any spectral signatures. Furthermore, we uncover a connection between the trapped charge and the existence of topological bound states localized at these defects. We test the robustness of these topological features when the protective crystalline symmetry is broken, and find that a single robust bound state can be localized at each disclination alongside the fractional charge. Our results conclusively show that disclination defects in TCIs can strongly trap fractional charges as well as topological bound states, and demonstrate the primacy of fractional charge as a probe of crystalline topology.

Exciting the domain wall soliton

Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start the study of these effects in the simplest configuration of a domain wall kink solution in the λ ϕ4 theory in 1+1 dimensions. We show that this solution has a single bound state and numerically study its slow decay rate in flat space. We then investigate the amplitude of this excitation by simulating a cosmological phase transition that leads to the formation of these kinks in an expanding universe. We find that kinks get formed with a 20% excess of energy with respect to their lowest energy configuration. We also explore the kink solution interacting with a thermal bath and extract the amplitude of the localized excitation as a function of temperature. We note that this amplitude increases with temperature but again the extra energy in the kink never goes over the 20% level. Finally, we argue that this extra energy may have important consequences in the subsequent evolution of defects in numerical simulations.

Scattering data and bound states of a squeezed double-layer structure

A heterostructure composed of two parallel homogeneous layers is studied in the limit as their widths l 1 and l 2, and the distance between them r shrinks to zero simultaneously. The problem is investigated in one dimension and the squeezing potential in the Schrödinger equation is given by the strengths V 1 and V 2 depending on the layer thickness. A whole class of functions V 1(l 1) and V 2(l 2) is specified by certain limit characteristics as l 1 and l 2 tend to zero. The squeezing limit of the scattering data a(k) and b(k) derived for the finite system is shown to exist only if some conditions on the system parameters V j , l j , j = 1, 2, and r take place. These conditions appear as a result of an appropriate cancellation of divergences. Two ways of this cancellation are carried out and the corresponding two resonance sets in the system parameter space are derived. On one of these sets, the existence of non-trivial bound states is proven in the squeezing limit, including the particular example of the squeezed potential in the form of the derivative of Dirac’s delta function, contrary to the widespread opinion on the non-existence of bound states in δ′-like systems. The scenario how a single bound state survives in the squeezed system from a finite number of bound states in the finite system is described in detail.

Ultrafast manipulation of the weakly bound helium dimer

Controlling the interactions between atoms with external fields opened up new branches in physics ranging from strongly correlated atomic systems to ideal Bose and Fermi gases and Efimov physics. Such control usually prepares samples that are stationary or evolve adiabatically in time. On the other hand, in molecular physics external ultrashort laser fields are employed to create anisotropic potentials that launch ultrafast rotational wave packets and align molecules in free space. Here we combine these two regimes of ultrafast times and low energies. We apply a short laser pulse to the helium dimer, a weakly bound and highly delocalized single bound state quantum system. The laser field locally tunes the interaction between two helium atoms, imparting an angular momentum of $2\hbar$ and evoking an initially confined dissociative wave packet. We record a movie of the density and phase of this wave packet as it evolves from the inside out. At large internuclear distances, where the interaction between the two helium atoms is negligible, the wave packet is essentially free. This work paves the way for future tomography of wave packet dynamics and provides the technique for studying exotic and otherwise hardly accessible quantum systems such as halo and Efimov states.

Studies of Dynamic Binding of Amino Acids to TiO2 Nanoparticle Surfaces by Solution NMR and Molecular Dynamics Simulations.

Adsorption of biomolecules onto material surfaces involves a potentially complex mechanism where molecular species interact to varying degrees with a heterogeneous material surface. Surface adsorption studies by atomic force microscopy, sum frequency generation spectroscopy, and solid-state NMR detect the structures and interactions of biomolecular species that are bound to material surfaces, which, in the absence of a solid-liquid interface, do not exchange rapidly between surface-bound forms and free molecular species in bulk solution. Solution NMR has the potential to complement these techniques by detecting and studying transiently bound biomolecules at the liquid-solid interface. Herein, we show that dark-state exchange saturation transfer (DEST) NMR experiments on gel-stabilized TiO2 nanoparticle (NP) samples detect several forms of biomolecular adsorption onto titanium(IV) oxide surfaces. Specifically, we use the DEST approach to study the interaction of amino acids arginine (Arg), lysine (Lys), leucine (Leu), alanine (Ala), and aspartic acid (Asp) with TiO2 rutile NP surfaces. Whereas Leu, Ala, and Asp display only a single weakly interacting form in the presence of TiO2 NPs, Arg and Lys displayed at least two distinct bound forms: a species that is surface bound and retains a degree of reorientational motion and a second more tightly bound form characterized by broadened DEST profiles upon the addition of TiO2 NPs. Molecular dynamics simulations indicate different surface bound states for both Lys and Arg depending on the degree of TiO2 surface hydroxylation but only a single bound state for Asp regardless of the degree of surface hydroxylation, in agreement with results obtained from the analysis of DEST profiles.

Deuteron Solid-State NMR Relaxation Measurements Reveal Two Distinct Conformational Exchange Processes in the Disordered N-Terminal Domain of Amyloid-β Fibrils.

We employed deuterium solid-state NMR techniques under static conditions to discern the details of the μs-ms timescale motions in the flexible N-terminal subdomain of Aβ1-40 amyloid fibrils, which spans residues 1-16. In particular, we utilized a rotating frame (R1ρ ) and the newly developed time domain quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) relaxation measurements at the selectively deuterated side chains of A2, H6, and G9. The two experiments are complementary in terms of probing somewhat different timescales of motions, governed by the tensor parameters and the sampling window of the magnetization decay curves. The results indicated two mobile "free" states of the N-terminal domain undergoing global diffusive motions, with isotropic diffusion coefficients of 0.7-1 ⋅ 108 and 0.3-3 ⋅ 106 ad2 s-1 . The free states are also involved in the conformational exchange with a single bound state, in which the diffusive motions are quenched, likely due to transient interactions with the structured hydrophobic core. The conformational exchange rate constants are 2-3 ⋅ 105 s-1 and 2-3 ⋅ 104 s-1 for the fast and slow diffusion free states, respectively.

Quantum mechanical potentials and inactive electron effects in charge exchange collisions

Scattering angle differential cross sections for the He+ + He single electron capture process are studied using plane wave Born approximation models for projectile energies between 180 keV and 1.89 MeV. Within this simplistic framework, we study the effects of the frozen core approximation by performing a full 5-Body calculation that explicitly includes all particles in the collision and comparing it with a single bound state model that neglects the bound electron in the projectile and a double bound state model that neglects the inactive electron in the target atom. Results are compared with experiment and we show that inclusion of the inactive electron in the perturbation potential is more important than inclusion in the wave functions. We also introduce a semi-quantum mechanical (SQM) perturbation potential that treats the atomic electrons as a quantum mechanical electron cloud rather than point particles. The SQM perturbation removes the deep, unphysical minimum that exists in cross sections calculated with Born-type models, but also has the effect of greatly reducing the magnitude of the small scattering angle cross sections.

A de Sitter tachyonic braneworld revisited

Within the framework of braneworlds, several interesting physical effects can be described in a wide range of energy scales, starting from high-energy physics to cosmology and low-energy physics. An usual way to generate a thick braneworld model relies in coupling a bulk scalar field to higher dimensional warped gravity. Quite recently, a novel braneworld was generated with the aid of a tachyonic bulk scalar field, having several remarkable properties. It comprises a regular and stable solution that contains a relevant 3-brane with de Sitter induced metric, arising as an exact solution to the 5D field equations, describing the inflationary eras of our Universe. Besides, it is asymptotically flat, despite of the presence of a negative 5D cosmological constant, which is an interesting feature that contrasts with most of the known, asymptotically either dS or AdS models. Moreover, it encompasses a graviton spectrum with a single massless bound state, accounting for 4D gravity localized on the brane, separated from the continuum of Kaluza-Klein massive graviton modes by a mass gap that makes the 5D corrections to Newton's law to decay exponentially. Finally, gauge, scalar and fermion fields are also shown to be localized on this braneworld. In this work, we show that this tachyonic braneworld allows for a nontrivial solution with a vanishing 5D cosmological constant that preserves all the above mentioned remarkable properties with a less amount of parameters, constituting an important contribution to the construction of a realistic cosmological braneworld model.

Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SU(3) flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of $\approx 806~\tt{MeV}$). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of L\"uscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The values of the leading-order low-energy scattering parameters in the irreducible representations of SU(3) are consistent with an approximate SU(6) spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between two baryons are constrained at this value of the quark masses, and their values indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible representations containing the $NN~({^1}S_0)$, $NN~({^3}S_1)$ and $\frac{1}{\sqrt{2}}(\Xi^0n+\Xi^-p)~({^3}S_1)$ channels unambiguously exhibit a single bound state, while the irreducible representation containing the $\Sigma^+ p~({^3}S_1)$ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of two-nucleon bound states at this value of the quark masses.

Noninteracting central site model: Localization and logarithmic entanglement growth

We investigate the stationary and dynamical behavior of an Anderson localized chain coupled to a single central bound state. The coupling to the central site partially dilutes the Anderson localized peak towards the nearly resonant sites. In particular, the number of resonantly coupled sites remains finite in the thermodynamic limit. This is further supported by a multifractal analysis of eigenstates that shows the frozen spectrum of fractal dimension, which is characteristic for localized phases in models with power-law hopping. Although the well-known Fano-resonance problem is seemingly similar to our system, it fails to describe it because of the absence of level repulsion within the energy spectrum. For weak coupling strengths to the central site, we identify a regime with a logarithmic in time transport of particles and information.

From supersymmetric quantum mechanics to scalar field theories

In this work we address the reconstruction problem, investigating the construction of field theories from supersymmetric quantum mechanics. The procedure is reviewed, starting from reflectionless potentials that admit one and two bound states. We show that, although the field theory reconstructed from the potential that support a single bound state is unique, it may break unicity in the case of two bound states. We illustrate this with an example, which leads us with two distinct field theories.

Bound states in string nets

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the zero-tension limit depending on the theory considered. In the latter case, we perturbatively compute the binding energy as a function of the total quantum dimension. We also address this issue in the honeycomb lattice where the number of bound states in the topological phase depends on the total quantum dimension. Finally, the internal structure of these bound states is analyzed in the zero-tension limit.

Stability of a tachyon braneworld

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be stable under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. The presence of this mass gap in the graviton spectrum makes the extra-dimensional corrections to Newton's law decay exponentially. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb's law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.

Quantum black hole formation in the BFSS matrix model

We study the various head-on collisions of two bunches of D0-branes and their real-time evolution in the BFSS matrix model in classical limit. For a various matrix size N respecting the 't Hooft scaling, we find quantitative evidence for the formation of a single bound state of D0-branes at late time, which is matrix model thermalization and dual to the formation of a larger black hole.