Particle Ground State Research Articles

Quasi-two-dimensional electron gas at the oxide interfaces for topological quantum physics

The development of “fault-tolerant” quantum computers, unaffected by noise and decoherence, is one of the fundamental challenges in quantum technology. One of the approaches currently followed is the realization of “topologically protected” qubits which make use of quantum systems characterized by a degenerate ground state of composite particles, known as “non-Abelian anyons”, able to encode and manipulate quantum information in a non-local manner. In this paper, we discuss the potential of quasi-two-dimensional electron gas (q2DEG) at the interface between band insulating oxides, like LaAlO3 and SrTiO3, as an innovative technological platform for the realization of topological quantum systems. Being characterized by a unique combination of unconventional spin-orbit coupling, magnetism, and 2D-superconductivity, these systems naturally possess most of the fundamental characteristics needed for the realization of a topological superconductor. These properties can be widely tuned by electric field effect acting on the orbital splitting and occupation of the non-degenerate 3d xy and 3d xz, yz bands. The topological state in oxide q2DEGs quasi-one-dimensional nanochannels could be therefore suitably controlled, leading to conceptual new methods for the realization of a topological quantum electronics based on the tuning of the orbital degrees of freedom.

One- and two-particle problem with correlated disorder potential

Motivated by the recent experimental and theoretical progresses in the exploration of the effect of disorder in interacting system, we examine the effect of two types of correlated disorder, the quasi-periodic potential and speckle disorder potential, on one- and two-particle problem with exact diagonalization (ED) method. We give the phase diagram for single particle in the presence of quasi-periodic potential and also analyse the effect of strong interaction on the phase diagram for ground state in two dimensions. For the speckle disorder potential case, we examine both the effect of correlation length and disorder strength on single particle ground state energy and two-particle binding energy. The transport property for different interaction strength under speckle disorder potential is also calculated and discussed at last.

Magnetic Force Microscopy Study of the Effect of Stresses on the Magnetic State of Ni Particles

The effect of strains on ferromagnetic particles has been studied. Arrays of Ni microparticles of different shapes on glass substrates have been fabricated. The magnetic state of the fabricated particles as a function of the degree of glass substrate bending has been investigated. It has been established that the ground state of unbent particles is vortex. It is shown that the substrate bending leads to the transition from the vortex to quasi-homogeneous state.

Impact of relativity on particle localizability and ground state entanglement

Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. In this paper, we examine these obstructions by tracing how they (partially) subside in passing to an approximation of ordinary quantum mechanics in the non-relativistic regime. We undertake a recovery of the characteristic features of non-relativistic quantum mechanics beyond simply the Schrödinger equation. We find that once this is achieved, there are persisting issues in the localizability of particle states. A major focus is on the lingering discrepancy between two different localization schemes in quantum field theory. The non-relativistic approximation of the quantum field theory is achieved by introducing an ultraviolet cutoff set by the Compton scale. The other main undertaking of this paper is to quantify the fate of ground state entanglement and the Unruh effect in the non-relativistic regime. Observing that the Unruh temperature vanishes in the naive limit as the speed of light is taken to infinity motivates the question: is the Unruh effect relativistic? It happens that this is closely related to the former issues, as ground state entanglement causes obstructions to localizability through the Reeh–Schlieder theorem.

МСМ исследование влияния механических напряжений на магнитное состояние частиц Ni

AbstractThe effect of strains on ferromagnetic particles has been studied. Arrays of Ni microparticles of different shapes on glass substrates have been fabricated. The magnetic state of the fabricated particles as a function of the degree of glass substrate bending has been investigated. It has been established that the ground state of unbent particles is vortex. It is shown that the substrate bending leads to the transition from the vortex to quasi-homogeneous state.

Микромагнитное моделирование магнитоупругого эффекта в субмикронных структурах

In the present work we study magnetoelastic effect in magnetic nanoparticles of elliptical, square and triangular shapes. Distribution of particles magnetization is investigated depending on their shape and the applied strain. Mechanical deformations lead to the appearance of new metastable states, and may change the particle ground state. The deformations significantly affect the distribution of the magnetization in the particles. This can be detected by magnetic force microscopy.

The α-quantization of lepton, quark and particle lifetimes

There are 196 elementary particles with well-measured lifetimes. Plotted logarithmically, they group into four Zones: (1) > 10−7 s; (2) 10−7–10−14 s; (3) 10−14–10−21 s; (4) 10−21–10−25 s, as follows: (1) neutron and muon; (2) quark ground-state particles with flavor-breaking electroweak decays: (3) quark ground-state particles with flavor-conserving and radiative decays; (4) short-lived excited states and high-energy W, Z, Higgs boson and t-quark states. Ground states have α-quantized lifetimes, while excited states occur with a continuum of values. An α-quantized lifetime grid is anchored on the π± lifetime, and extends over 12 powers of α, where α−1 ~ 137 is the fine structure constant. Ground-state lifetimes separate into (u,d), s, c, b flavor groups, each dominated by a single quark, in accordance with the rule (u,d) > s > b > c. Flavor-breaking lifetimes are longer than flavor-conserving lifetimes by a factor of ~ α−4. Each Zone (2) flavor group has a central lifetime, and deviations occur as integer factors of ~ 2, 3, or 4. This observed lifetime α-dependence is conjugate to an observed mass/energy α-dependence.

Finite-temperature phases of two-dimensional spin-orbit-coupled bosons

We determine the finite temperature phase diagram of two dimensional bosons with two hyperfine (pseudo-spin) states coupled via Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berenzinskii-Kosterlitz-Thouless superfluid phase with quasi-long range order. We show that the spin-order of the quasi-condensate is driven by the anisotropy of interparticle interaction, favoring either a homogeneous plane wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin density correlation function. For fully isotropic interparticle interaction, our calculations indicate a fractionalized quasi-condensate where the mean-field degeneracy of plane wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a cross-over remains for finite size systems.

How cube-like must magnetic nanoparticles be to modify their self-assembly?

Systems whose magnetic response can be finely tuned using control parameters, such as temperature and external magnetic field strength, are extremely desirable, functional materials. Magnetic nanoparticles, in particular suspensions thereof, offer opportunities for this controllability to be realised. Cube-like particles are particularly mono-disperse examples that, together with their favourable packing behaviour, make them of significant interest for study. Using a combination of analytical calculations and molecular dynamics we have studied the self-assembly of permanently magnetised dipolar superballs. The superball shape parameter was varied in order to interpolate the region between the already well-studied sphere system and that of the recently investigated cube. Our findings show that as a superball particle becomes more cubic the chain to ring transition, observed in the ground state of spherical particles, occurs at an increasingly larger cluster size. This effect is mitigated, however, by the appearance of a competing configuration; asymmetric rings, a conformation that we show superballs can readily adopt.

Correlation energy for elementary bosons: Physics of the singularity

We propose a compact perturbative approach that reveals the physical origin of the singularity occurring in the density dependence of correlation energy: like fermions, elementary bosons have a singular correlation energy which comes from the accumulation, through Feynman “bubble” diagrams, of the same non-zero momentum transfer excitations from the free particle ground state, that is, the Fermi sea for fermions and the Bose–Einstein condensate for bosons. This understanding paves the way toward deriving the correlation energy of composite bosons like atomic dimers and semiconductor excitons, by suggesting Shiva diagrams that have similarity with Feynman “bubble” diagrams, the previous elementary boson approaches, which hide this physics, being inappropriate to do so.

Incompressibility Estimates for the Laughlin Phase, Part II

We consider fractional quantum Hall states built on Laughlin’s original N-body wave-functions, i.e., they are of the form holomorphic × Gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear naturally when looking for the ground state of 2D particles in strong magnetic fields, interacting via repulsive forces and subject to an external potential due to trapping and/or disorder. We prove that all functions in this class satisfy a universal local density upper bound, in a suitable weak sense. Such bounds are useful to investigate the response of fractional quantum Hall phases to variations of the external potential. Contrary to our previous results for a restricted class of wave-functions, the bound we obtain here is not optimal, but it does not require any additional assumptions on the wave-function, besides analyticity and symmetry of the pre-factor modifying the Laughlin function.

Uniqueness of density-to-potential mapping for fermionic lattice systems

We demonstrate that, for a fermionic lattice system, the ground-state particle density uniquely determines the external potential except for the sites corresponding to nodes of the wave function, and the limiting case where the Pauli exclusion principle completely determines the occupation of all sites. Our fundamental finding completes, for this general class of systems, the one-to-one correspondence between ground states, their densities, and the external potential at the base of the Hohenberg-Kohn theorem. Moreover we demonstrate that the mapping from wave function to potential is unique not just for the ground state, but also for excited states. To illustrate our findings, we develop a practical inversion scheme to determine the external potential from a given density. Our results hold for a general class of lattice models, which includes the Hubbard model.

On the oscillator realization of conformal U(2, 2) quantum particles and their particle-hole coherent states

We revise the unireps. of U(2, 2) describing conformal particles with continuous mass spectrum from a many-body perspective, which shows massive conformal particles as compounds of two correlated massless particles. The statistics of the compound (boson/fermion) depends on the helicity h of the massless components (integer/half-integer). Coherent states (CS) of particle-hole pairs (“excitons”) are also explicitly constructed as the exponential action of exciton (non-canonical) creation operators on the ground state of unpaired particles. These CS are labeled by points Z (2 × 2 complex matrices) on the Cartan-Bergman domain \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_4=U(2,2)/U(2)^2$\end{document}D4=U(2,2)/U(2)2, and constitute a generalized (matrix) version of Perelomov U(1, 1) coherent states labeled by points z on the unit disk \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_1=U(1,1)/U(1)^2$\end{document}D1=U(1,1)/U(1)2. First, we follow a geometric approach to the construction of CS, orthonormal basis, U(2, 2) generators and their matrix elements and symbols in the reproducing kernel Hilbert space \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}_\lambda (\mathbb {D}_4)$\end{document}Hλ(D4) of analytic square-integrable holomorphic functions on \documentclass[12pt]{minimal}\begin{document}$\mathbb {D}_4$\end{document}D4, which carries a unitary irreducible representation of U(2, 2) with index \documentclass[12pt]{minimal}\begin{document}$\lambda \in \mathbb {N}$\end{document}λ∈N (the conformal or scale dimension). Then we introduce a many-body representation of the previous construction through an oscillator realization of the U(2, 2) Lie algebra generators in terms of eight boson operators with constraints. This particle picture allows us for a physical interpretation of our abstract mathematical construction in the many-body jargon. In particular, the index λ is related to the number 2(λ − 2) of unpaired quanta and to the helicity h = (λ − 2)/2 of each massless particle forming the massive compound.

Magnetic particles confined in a modulated channel: structural transitions tunable by tilting a magnetic field.

The ground state of colloidal magnetic particles in a modulated channel are investigated as a function of the tilt angle of an applied magnetic field. The particles are confined by a parabolic potential in the transversal direction while in the axial direction a periodic substrate potential is present. By using Monte Carlo simulations, we construct a phase diagram for the different crystal structures as a function of the magnetic field orientation, strength of the modulated potential, and the commensurability factor of the system. Interestingly, we found first- and second-order phase transitions between different crystal structures, which can be manipulated by the orientation of the external magnetic field. A reentrant behavior is found between two- and four-chain configurations, with continuous second-order transitions. Novel configurations are found consisting of frozen solitons of defects. By changing the orientation and/or strength of the magnetic field and/or the strength and periodicity of the substrate potential, the system transits through different phases.

Erratum to: Overview on Solid 4He and the Issue of Supersolidity

In the original article, the text in Sect. 6.1.9 on page 350 has a misplaced reference in addition to a sentence missing. The two sentences “On the basis of many-body theory starting from localized orbitals for 4He, Anderson has argued that necessarily the ground state of boson particles has defects. This work is summarized in a paper in these special issues [212]” should be replaced by the following: “On the basis of many-body theory starting from localized orbitals for 4He, Anderson has argued that necessarily the ground state of boson particles has defects [234, 296]. In a paper in these special issues [212], Anderson argues that, even in absence of defects, exchange processes of bosons in the solid are enough to establish a local phase so that the system has vortex-like excitations. From an analysis of the Boson Hubbard model, he argues [297, 212] that this system at the lowest temperatures is in a novel state of matter that has superflow, but not ODLRO, and he conjectures that a similar state is present in solid 4He with vortex excitations essentially decoupled from phonons. This possibility warrants further deep theoretical investigations”.

Structure of the phonon vacuum state

The action of the long-range residual force on the expectation value of observables in the nuclear ground states is evaluated by finding optimal values for the coefficients of the canonical transformation which connects the phonon vacuum state with the (quasi)particle ground state. After estimating the improvements over the predictions of the independent-particle approximation we compare the ground-state wave functions, obtained using the presented approach, with those obtained using the conventional random phase approximation (RPA) and its extended version. The problem with overbinding of the nuclear ground state calculated using the RPA is shown to be removed if one sticks to the prescriptions of the present approach. The reason being that the latter conforms to the original variational formulation. Calculations are performed within the two-level Lipkin-Meshkov-Glick model in which we present results for the ground and first excited state energies as well as for the ground-state particle occupation numbers.

Manifestation of the light-induced drift effect in chemically peculiar stellar atmospheres

We have calculated the factor (νg − νe)/νg in the temperature range T = 300–20 000 K for the ions Be+, Mg+, Ca+, C+ in atomic hydrogen and for the ions Mg+ in atomic argon using the known interaction potentials. Here νe and νg are the transport collision frequencies for excited- and ground-state particles respectively. Calculations have shown that at T = 10 000–20 000 K, typical temperatures of the atmospheres of chemically peculiar (CP) stars, the values |νg − νe|/νg ≈ 0.1–0.2 can be reached for ions. This causes the light-induced drift (LID) velocity of ions up to ∼0.1 cm/s in the atmospheres of CP stars with temperatures T T > 10 000 K) it is possible to expect approximately identical magnitude of the LID effect and that of radiation pressure. In the very hot stars (T >20 000 K) the LID effect is manifested very weakly.

Crystalline multilayers of charged colloids in soft confinement: experiment versus theory

We combine real-space experiments and lattice sum calculations to investigate the phase diagram of charged colloidal particles under soft confinement. In the experiments we explore the equilibrium phase diagram of charged colloidal spheres in aqueous suspensions confined between two parallel charged walls at low background salt concentrations. Motivated by the experiments, we perform lattice sum minimizations to predict the crystalline ground state of point-like Yukawa particles which are exposed to a soft confining wall potential. In the multilayered crystalline regime, we obtain good agreement between the experimental and numerical findings: upon increasing the density we recover the sequence 2□ → 2△ → 2hcp⊥ → 3□ → 3△ → 3hcp⊥ → 4□.

Temporal first- and second-order correlations in a polariton condensate

We analyze the decay of the first- and second-order correlations, ${g}^{(1)}(t)$ and ${g}^{(2)}(t)$, using a Langevin equation of the order parameter for polaritons in a microcavity, pumped nonresonantly with a noise-free laser diode. We consider a coupling of the condensate to the excited states by two types of scattering mechanism both derived from the polariton-polariton interaction: (a) one particle is scattered from an excited state to the ground state, while another excited-state particle is scattered to a higher-energy state, and (b) two ground-state particles are scattered into low-lying excited states with opposite momenta. This nonresonant scattering rate increases with the condensate population. We calculate from the Langevin equation for the order parameter the temporal decay of ${g}^{(1)}(t)$ and the linewidth $\ensuremath{\kappa}$ analytically. Our results make close contacts with the linewidth enhancement factor well known from semiconductor lasers. A semiclassical evaluation for the polariton kinetics yields a first-order correlation function, which is in good agreement with experimental results and with the results of Schwendimann and Quattropani, although our formulation is more complete because it contains also the dispersive effects of both types of scattering processes and uses no fitting parameters. Our analysis also provides an understanding of the rather different pump dependencies of the linewidth reported in the literature. The calculated second-order correlation function ${g}^{(2)}(0)$ is shown to stay for larger pump values as observed on a plateau above the coherent limit again due to the nonresonant scattering processes.

The Gross–Pitaevskii Functional with a Random Background Potential and Condensation in the Single Particle Ground State

For discrete and continuum Gross–Pitaevskii energy functionals with a random background potential, we study the Gross–Pitaevskii ground state. We characterize a regime of interaction coupling when the Gross–Pitaevskii ground state and the ground state of the random background Hamiltonian asymptotically coincide.