One-particle States Research Articles

Massive spin-one-half one-particle states for the mass-dimension-one fermions

We study the conditions under which a non-standard Wigner class concerning discrete symmetries may arise for massive spin-one-half states. The mass-dimension-one fermionic states are shown to constitute explicit examples. We also show how to conciliate these states with the current criticism due to the Lee and Wick, and Weinberg formulation.

The Atomic Density on the Thomas—Fermi Length Scale for the Chandrasekhar Hamiltonian

We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an observation by Fefferman and Seco (1989), we find that the density on this scale converges to the minimizer of the Thomas--Fermi functional of hydrogen as $Z\to\infty$ when $Z/c$ is fixed to a value not exceeding $2/\pi$. This shows that the electron density on the Thomas--Fermi length scale does not exhibit any relativistic effects.

Antiferromagnetism, Superconductivity and Phase Diagram in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model III—

We investigate the ground-state phase diagram of the two-dimensional Hubbard model based on the optimization variational Monte Carlo method. We use a wave function that is an off-diagonal type given as $\psi=\exp(-\lambda K)P_G\psi_0$, where $\psi_0$ is a one-particle state, $P_G$ is the Gutzwiller operator, $K$ is the kinetic operator, and $\lambda$ is a variational parameter. The many-body effect plays an important role as an origin of spin correlation and superconductivity in correlated electron systems. We examine the competition between the antiferromagnetic state and superconducting state by varying the Coulomb repulsion $U$, the band parameter $t'$ and the electron density $n_e$. We show a phase diagram that includes superconducting and antiferromagnetic phases and that $t'=0$ is most favorable for superconductivity.

On Bose–Einstein Condensation in the Luttinger–Sy Model with Finite Interaction Strength

We study Bose-Einstein condensation (BEC) in the Luttinger-Sy model. Here, Bose point particles in one spatial dimension do not interact with each other, but, through a positive (repulsive) point potential with impurities which are randomly located along the real line according to the points of a Poisson process. Our emphasis is on the case in which the interaction strength is not infinite. As a main result, we prove that in thermal equilibrium the one-particle ground state is macroscopically occupied, provided that the particle density is larger than a critical one depending on the temperature.

Bulk entanglement entropy in perturbative excited states

We compute the bulk entanglement entropy across the Ryu-Takayanagi surface for a one-particle state in a scalar field theory in AdS_33. We work directly within the bulk Hilbert space and include the spatial spread of the scalar wavefunction. We give closed form expressions in the limit of small interval sizes and compare the result to a CFT computation of entanglement entropy in an excited primary state at large cc. Including the contribution from the backreacted minimal area, we find agreement between the CFT result and the FLM and JLMS formulas for quantum corrections to holographic entanglement entropy. This provides a non-trivial check in a state where the answer is not dictated by symmetry. Along the way, we provide closed-form expressions for the scalar field Bogoliubov coefficients that relate the global and Rindler slicings of AdS_33.

The Gibbs Paradox.

The Gibbs Paradox is essentially a set of open questions as to how sameness of gases or fluids (or masses, more generally) are to be treated in thermodynamics and statistical mechanics. They have a variety of answers, some restricted to quantum theory (there is no classical solution), some to classical theory (the quantum case is different). The solution offered here applies to both in equal measure, and is based on the concept of particle indistinguishability (in the classical case, Gibbs’ notion of ‘generic phase’). Correctly understood, it is the elimination of sequence position as a labelling device, where sequences enter at the level of the tensor (or Cartesian) product of one-particle state spaces. In both cases it amounts to passing to the quotient space under permutations. ‘Distinguishability’, in the sense in which it is usually used in classical statistical mechanics, is a mathematically convenient, but physically muddled, fiction.

Fermionic one-particle states in curved spacetimes

We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin frac{1}{2} fields. A curved spacetime can be equipped with a coordinate system in which the metric component g−− = 0. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector ∂− and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Minkowski spacetime. Therefore, it can be interpreted in terms of one-particle states and the corresponding vacuum state similarly to the second quantization in Minkowski spacetime.

Effective Control of Chemical Potentials by Rabi Coupling with RF-Fields in Ultracold Mixtures

We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. This term is easily realized by Rabi coupling between different hyperfine levels of the same atomic species. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained by diagonalizing the mixing matrix of the Rabi term. This way of controlling the chemical potentials applies to both bosonic and fermionic atoms and it also allows for spatially- and temporally-dependent imbalances. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions.

Probing Wigner rotations for any group

Wigner rotations are transformations that affect spinning particles and cause the observable phenomenon of Thomas precession. Here we study these rotations for arbitrary symmetry groups with a semi-direct product structure. In particular we establish a general link between Wigner rotations and Thomas precession by relating the latter to the holonomies of a certain Berry connection on a momentum orbit. Along the way we derive a formula for infinitesimal, Lie-algebraic transformations of one-particle states.

Single and multiple Auger decay processes from the Ne+1s−12p−1np shake-up states studied with a multielectron coincidence method

The single, double, and triple Auger decay processes from the $1{s}^{\ensuremath{-}1}2{p}^{\ensuremath{-}1}np$ shake-up states of Ne have been studied with a multielectron coincidence method. It is revealed that the Rydberg electron promoted in the initial photoionization step generally acts as a spectator both in the single and double Auger decays. The single Auger decay predominantly produces three-hole one-particle final states while leaving the Rydberg electron virtually unchanged. In the cascade double Auger paths, the Rydberg electron is a spectator in the first step of the cascade process but is subsequently released in the second step, leading to the formation of three-hole final states. The direct paths of double Auger decays, which are much weaker than the cascade paths, produce preferably four-hole one-particle states due to the spectator behavior of the Rydberg electron. The distributions of the $\mathrm{N}{\mathrm{e}}^{4+}$ states populated by the triple Auger decays are also presented.

Interband Absorption and Photoluminescence in the Cylindrical Layered CdS/HgS/CdS Heterostructure

Within the approximation of an isotropic effective mass, the one-particle states of charge carriers in the layered CdS/HgS/CdS heterostructure are considered. It is shown that under conditions in which the strong-quantization regime is realized in the HgS layer, the spatial localization of charge carriers is realized there with the maximum probability. The energy spectrum and envelopes of the wave functions of the electron and hole states are computed in the structure under consideration. The interband optical absorption is computed, when the system is a layered cylindrical quantum dot and when there is a free motion of the charge carriers along the symmetry axis. For the same cases, the photoluminescence spectrum is also considered.

On the observability of Pauli crystals in experiments with ultracold trapped Fermi gases

The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high-order correlations in systems of many identical fermions and is responsible for a particular geometric arrangement of trapped particles even when all mutual interactions are absent. These geometric structures, called Pauli crystals, are predicted for a system of N identical atoms trapped in a harmonic potential. They emerge as the most frequent configurations in a collection of single-shot pictures of the system. Here we study how fragile Pauli crystals are when realistic experimental limitations are taken into account. The influence of the number of single-shots pictures available to analysis, thermal fluctuations and finite efficiency of detection are considered. The role of these sources of noise on the possibility of experimental observation of Pauli crystals is shown and conditions necessary for the detection of the geometrical arrangements of particles are identified.

Pairing theory for strongly correlated d -wave superconductors

Motivated by recent proposals of correlation induced insensitivity of $d$-wave superconductors to impurities, we develop a simple pairing theory for these systems for up to a moderate strength of disorder. Our description implements the key ideas of Anderson, originally proposed for disordered $s$-wave superconductors, but in addition takes care of the inherent strong electronic repulsion in these compounds, as well as disorder induced inhomogeneities. We first obtain the self-consistent one-particle states, which capture the effects of disorder exactly, and strong correlations using Gutzwiller approximation. These ``normal states,'' representing the interplay of strong correlations and disorder, when coupled through pairing attractions following the path of Bardeen-Cooper-Schrieffer (BCS), produce results nearly identical to those from a more sophisticated inhomogeneous Hartree-Fock-Bogoliubov analysis that takes care of strong electronic repulsions.

Prospects of Anderson's theorem for disordered cuprate superconductors

We develop a simple pairing theory of superconductivity in strongly correlated d-wave superconductors for up to a moderate strength of disorder. Our description implements the key ideas of Anderson, originally proposed for disordered s-wave superconductors, but in addition takes care of the inherent strong electronic repulsion in these compounds, as well as the inhomogeneities. We first obtain the self-consistent one-particle states, that capture the effects of disorder exactly, and strong correlations using Gutzwiller approximation. These ‘normal states’ (at zero temperature) when coupled through BCS-type pairing attractions, produces results which are nearly identical to those from a more sophisticated Gutzwiller augmented Bogoliubov-de Gennes analysis.

Strongly absorbing light nanostructures containing metal quantum dots

In the framework of dipole approximation, it is shown that the oscillator strengths of transitions as well as the dipole moments for transitions for one-particle electron Coulomb states emerging above the spherical surface quantum dot of metal assume giant values considerably (by two orders of magnitude) exceeding the typical values of the corresponding quantities for dielectrics. It has been established that the giant values of the light absorption cross section in the nanosystems under investigation make it possible to use such nanosystems as strongly absorbing nanomaterials in a wide range of infrared waves with a wavelength that can be varied in a wide range depending on the type of contacting materials.

Universal upper bounds on the Bose-Einstein condensate and the Hubbard star

For $N$ hard-core bosons on an arbitrary lattice with $d$ sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by ${N}_{\text{max}}=(N/d)(d\ensuremath{-}N+1)$. This bound can only be attained for one-particle states $|\ensuremath{\varphi}\ensuremath{\rangle}$ with equal amplitudes with respect to the hard-core basis (sites) and when the corresponding $N$-particle state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is maximally delocalized. This result is generalized to the maximum condensate possible within a given sublattice. We observe that such maximal local condensation is only possible if the mode entanglement between the sublattice and its complement is minimal. We also show that the maximizing state $|\mathrm{\ensuremath{\Psi}}\ensuremath{\rangle}$ is related to the ground state of a bosonic ``Hubbard star'' showing Bose-Einstein condensation.

Remarks on a gauge theory for continuous spin particles

We discuss in a systematic way the gauge theory for a continuous spin particle proposed by Schuster and Toro. We show that it is naturally formulated in a cotangent bundle over Minkowski spacetime where the gauge field depends on the spacetime coordinate {x^mu } and on a covector eta _mu . We discuss how fields can be expanded in eta _mu in different ways and how these expansions are related to each other. The field equation has a derivative of a Dirac delta function with support on the eta -hyperboloid eta ^2+1=0 and we show how it restricts the dynamics of the gauge field to the eta -hyperboloid and its first neighbourhood. We then show that on-shell the field carries one single irreducible unitary representation of the Poincaré group for a continuous spin particle. We also show how the field can be used to build a set of covariant equations found by Wigner describing the wave function of one-particle states for a continuous spin particle. Finally we show that it is not possible to couple minimally a continuous spin particle to a background abelian gauge field, and we make some comments about the coupling to gravity.

Multihole edge states in Su-Schrieffer-Heeger chains with interactions

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V=t2 vs. t1=t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and non-trivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a non-interacting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of topological edge states in the equivalent chain can be readily identifed, as well as their correspondence to the original two-hole states. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).

Nonlinear Correction to Absorption Spectrum under Irradiation of Microwave Field in Conventional BCS Superconductors

We investigate the absorption spectrum of s-wave superconductors under microwave pump field irradiation. The third-order response function is calculated in the dirty limit with the electron–phonon interaction included at finite temperatures. We find that the nonlinear correction to the linear absorption shows peculiar behavior when the pump field frequency is smaller than the superconducting gap. At finite temperatures, a negative nonlinear correction exists, which is caused by thermally excited quasiparticles. The vertex correction by impurity scattering is found to contain a dissipation mechanism by inelastic scattering (interaction between electrons and acoustic phonons) or nonlocality. We need this mechanism to obtain finite absorption in a nonequilibrium stationary state under a monochromatic external field. Although this term originates from the deformation of a one-particle state, there is also a final-state interaction (the amplitude mode). The latter term represents two-photon excitation and is a...

(t, n) Threshold Quantum State Sharing Scheme Based on Linear Equations and Unitary Operation

Quantum state sharing (QSTS) plays an important role in transporting, managing, and distributing keys. In this paper, by adopting the linear equation instead of using the Lagrange interpolation, a new idea of constructing (t, n) threshold quantum state sharing scheme is proposed. The best innovation is that a new tool in constructing (t, n) threshold structure is proposed. In this scheme, the dealer who possesses a sequence of one-particle unknown quantum states intends to share it with n participants and authorizes t out of them cooperate to reconstruct the sequence. First, the equations decided by the private key of dealer are constructed. Second, the dealer distributes the private keys of n participants by using the solutions to the equations just mentioned. Finally, the dealer encodes the sequence through a unitary operation, and any t out of the n participants recover the initial quantum state sequence through the unitary operations decided by the solutions to the linear equations. Compared to the existing schemes, the proposed scheme is easily realized in physical experiment, and its successful probability is 100% theoretically.