LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS

We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

Ground states for asymptotically periodic quasilinear Schrdinger equations with critical growth

For a class of asymptotically periodic quasilinear Schr？dinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schr？dinger equations are reduced to semilinear Schr？dinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schr？dinger equations and the quasilinear Schr？dinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schr？dinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schr？dinger equations.

Transparently manipulating spin-orbit qubit via exact degenerate ground states

By investigating a harmonically confined and periodically driven particle system with spin-orbit coupling(SOC)and a specific controlled parameter,we demonstrate an exactly solvable two-level model with a complete set of spin-motion entangled Schrödinger kitten(or cat)states.In the undriven case,application of a modulation resonance results in the exact stationary states.We show a decoherence-averse effect of SOC and implement a transparent coherent control by exchanging positions of the probability-density wavepackets to create transitions between the different degenerate ground states.The expected energy consisting of quantum and continuous parts is derived,and the energy deviations caused by the exchange operations are much less than the quantum gap.The results could be directly extended to a weakly coupled single-particle chain for transparently encoding spin-orbit qubits via the robust spin-motion entangled degenerate ground states.

GROUND STATES OF A NONLINEAR ELLIPTICSYSTEM IN R^N

We investigate existence of ground states of nonlinear elliptic systems in R-N and establish decaying laws for solutions of the systems at infinity.

Neural network study of the nuclear ground-state spin distribution within a random interaction ensemble

The distribution of the nuclear ground-state spin in a two-body random ensemble(TBRE)was studied using a general classification neural network(NN)model with two-body interaction matrix elements as input features and the corresponding ground-state spins as labels or output predictions.The quantum many-body system problem exceeds the capability of our optimized NNs in terms of accurately predicting the ground-state spin of each sample within the TBRE.However,our NN model effectively captured the statistical properties of the ground-state spin because it learned the empirical regularity of the ground-state spin distribution in TBRE,as discovered by physicists.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

NOTE ON GROUND STATES OF NONLINEAR SCHRODINGER SYSTEMS

We give sufficient and necessary conditions for the existence and nonexistence of positive ground state solutions of a class of coupled nonlinear Schroedinger equations.

Ground States of K-component Coupled Nonlinear Schrödinger Equations with Inverse-square Potential

In this paper,the authors study ground states for a class of K-component coupled nonlinear Schrödinger equations with a sign-changing potential which is periodic or asymptotically periodic.The resulting problem engages three major difficulties:One is that the associated functional is strongly indefinite,the second is that,due to the asymptotically periodic assumption,the associated functional loses the Z^(N)-translation invariance,many effective methods for periodic problems cannot be applied to asymptotically periodic ones.The third difficulty is singular potentialμ/(|x|)^(2),which does not belong to the Kato’s class.These enable them to develop a direct approach and new tricks to overcome the difficulties caused by singularity and the dropping of periodicity of potential.

Remark on Exponential Decay of Ground States for N-Laplacian Equations

We study exponential decay property of radial ground states to a class of N-Laplacian elliptic equations in the whole space R^N. Their decay rates as /x/→∞ are obtained explicitly.

Ground State, Isoelectronic Ions and Low-Lying Excited States of Lithium Atom in Strong Magnetic Field

In the framework of the variational Monte Carlo method, the ground states of the lithium atom and lithium like ions up to Z = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states , and of the lithium atom in strong magnetic field are also investigated. Simple trial wave functions for lithium are used.

Spectral fine structure of the atomic ground states based on full relativistic theory

We focus on the full relativistic quantum mechanical calculations from boron to fluorine atoms with electronic configuration of 1s^22s^22p^n （n = 1, 2, 3, 4, and 5）, where ls^22s^2 is the closed shell and 2pn is the open shell. Their active electrons in the open shell occupy all the six spinors as far as possible. Therefore, we suggest a new rule called ＂maximum probability＂ for the full symmetry group relativistic theory. Furthermore, the spectral fine structure of the atomic ground states based on the full relativistic theory and their intervals of L-S splitting are all reasonable. It is impossible to calculate the L-S splitting through non-relativistic quantum mechanics. The relativistic effect of atomic mass is increased significantly by about 12 folds from boron atom to fluorine atom.

Ground States of Ultracold Spin-1 Atoms in a Deep Double-Well Optical Superlattice in a Weak Magnetic Field

The ground states of the ultracold spin-1 atoms superlattice in a weak magnetic field are obtained. It is shown trapped in a deep one-dimensional double-weU optical that the ground-state diagrams of the reduced double- well model are remarkably different for the antiferromagnetic and ferromagnetic condensates. The transition between the singlet state and nematic state is observed for the antiferromagnetic interaction atoms, which can be realized by modulating the tunneling parameter or the quadratic Zeeman energy. An experiment to distinguish the different spin states is suggested.

Analysis of the energy spectra of ground states of deformed nuclei in the rare-earth region

The 62Sm, 64Gd, 66Dy, 70Yb, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found that the low-lying spectra of ground band states are in good agreement with the experimental data.

Nonexistence of Ground States of-△u=u^p-u^q

The authors use the method of moving spheres to prove the nonexistence of ground states of -△u = u^p - u^q for n≥3,-∞〈p〈（n＋2）/（n-2） and q〉max （1,p）, In fact this conclusion is a special case of -△u =f（u） for n≥2.

On Existence of Ground States for Some Elliptic Systems

In this paper we consider the existence of ground states for some 2- coupled nonlinear Schrodinger systems with or without potentials. Under various conditions on the parameters in the equations, we prove the existence of ground states.

THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRODINGER SYSTEMS

In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].

Magnetic ground state of plutonium dioxide: DFT+U calculations

The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

Sympathetic electromagnetically induced transparency ground state cooling of a~(40)Ca^(+)–~(27)Al^(+)pair in an~(27)Al^(+)clock

We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.