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Journal articles on the topic 'Schrödinger–Hardy systems'

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Author: Grafiati

Published: 10 March 2023

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1

Pucci, Patrizia. "Critical Schrödinger-Hardy systems in the Heisenberg group." Discrete & Continuous Dynamical Systems - S 12, no. 2 (2019): 375–400. http://dx.doi.org/10.3934/dcdss.2019025.

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2

Fiscella, Alessio, Patrizia Pucci, and Binlin Zhang. "p-fractional Hardy–Schrödinger–Kirchhoff systems with critical nonlinearities." Advances in Nonlinear Analysis 8, no. 1 (June 30, 2018): 1111–31. http://dx.doi.org/10.1515/anona-2018-0033.

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Abstract This paper deals with the existence of nontrivial solutions for critical Hardy–Schrödinger–Kirchhoff systems driven by the fractional p-Laplacian operator. Existence is derived as an application of the mountain pass theorem and the Ekeland variational principle. The main features and novelty of the paper are the presence of the Hardy terms as well as critical nonlinearities.

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3

Bordoni, Sara, and Patrizia Pucci. "Schrödinger–Hardy systems involving two Laplacian operators in the Heisenberg group." Bulletin des Sciences Mathématiques 146 (July 2018): 50–88. http://dx.doi.org/10.1016/j.bulsci.2018.03.001.

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4

Faraci, Francesca, Csaba Farkas, and Alexandru Kristály. "Multipolar Hardy inequalities on Riemannian manifolds." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 2 (January 26, 2018): 551–67. http://dx.doi.org/10.1051/cocv/2017057.

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We prove multipolar Hardy inequalities on complete Riemannian manifolds, providing various curved counterparts of some Euclidean multipolar inequalities due to Cazacu and Zuazua [Improved multipolar Hardy inequalities, 2013]. We notice that our inequalities deeply depend on the curvature, providing (quantitative) information about the deflection from the flat case. By using these inequalities together with variational methods and group-theoretical arguments, we also establish non-existence, existence and multiplicity results for certain Schrödinger-type problems involving the Laplace-Beltrami operator and bipolar potentials on Cartan-Hadamard manifolds and on the open upper hemisphere, respectively.

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5

Fiscella, Alessio, Patrizia Pucci, and Sara Saldi. "Existence of entire solutions for Schrödinger–Hardy systems involving two fractional operators." Nonlinear Analysis 158 (July 2017): 109–31. http://dx.doi.org/10.1016/j.na.2017.04.005.

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6

Wang, Guotao, and Xueyan Ren. "Radial symmetry of standing waves for nonlinear fractional Laplacian Hardy–Schrödinger systems." Applied Mathematics Letters 110 (December 2020): 106560. http://dx.doi.org/10.1016/j.aml.2020.106560.

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7

Zhang, Jian, and Wen Zhang. "Existence and asymptotic behavior of ground states for Schrödinger systems with Hardy potential." Nonlinear Analysis 189 (December 2019): 111586. http://dx.doi.org/10.1016/j.na.2019.111586.

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8

ADIMURTHI. "BEST CONSTANTS AND POHOZAEV IDENTITY FOR HARDY–SOBOLEV-TYPE OPERATORS." Communications in Contemporary Mathematics 15, no. 03 (May 19, 2013): 1250050. http://dx.doi.org/10.1142/s0219199712500502.

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This paper is threefold. Firstly, we reformulate the definition of the norm induced by the Hardy inequality (see [J. L. Vázquez and N. B. Zographopoulos, Functional aspects of the Hardy inequality. Appearance of a hidden energy, preprint (2011); http://arxiv. org/abs/1102.5661]) to more general elliptic and sub-elliptic Hardy–Sobolev-type operators. Secondly, we derive optimal inequalities (see [C. Cowan, Optimal inequalities for general elliptic operator with improvement, Commun. Pure Appl. Anal.9(1) (2010) 109–140; N. Ghoussoub and A. Moradifam, Bessel pairs and optimal Hardy and Hardy–Rellich inequalities, Math. Ann.349(1) (2010) 1–57 (electronic)]) for multiparticle systems in ℝN and Heisenberg group. In particular, we provide a direct proof of an optimal inequality with multipolar singularities shown in [R. Bossi, J. Dolbeault and M. J. Esteban, Estimates for the optimal constants in multipolar Hardy inequalities for Schrödinger and Dirac operators, Commun. Pure Appl. Anal.7(3) (2008) 533–562]. Finally, we prove an approximation lemma which allows to show that the domain of the Dirichlet–Laplace operator is dense in the domain of the corresponding Hardy operators. As a consequence, in some particular cases, we justify the Pohozaev-type identity for such operators.

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9

DE ANGELIS, GIAN FABRIZIO. "PATH INTEGRALS FOR QUBITS." International Journal of Modern Physics B 18, no. 04n05 (February 20, 2004): 617–22. http://dx.doi.org/10.1142/s0217979204024239.

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Feynman started the theory of quantum computation by observing that quantum mechanical amplitudes cannot be simulated efficiently on a computer, since path integrals are computationally hard. Path integrals are heuristic tools for Schrödinger's hamiltonians, at least for real time dynamics. On the contrary they have a rigorous mathematical meaning for quantum systems which are worth a finite but no matter how large number of qubits.

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10

Anaya-Morales, A., and F. Delgado. "Enquiring Electronic Structure Using Quantum Computers: Hands on Qiskit." Journal of Physics: Conference Series 2448, no. 1 (February 1, 2023): 012014. http://dx.doi.org/10.1088/1742-6596/2448/1/012014.

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Abstract Solving the electronic structure for multi-electronic systems is a hard problem. Even for small atoms and molecules, approximations have to be made in order to solve numerically the Schrödinger equation. Although different methods have been developed to take into account electron correlations, their computational cost reduces their feasibility. Quantum simulation provides an alternative to traditional computational methods for enquiring the electronic structure of molecules. Specifically, the Variational Quantum Eigensolver (VQE) algorithm provides a hybrid quantum-classical algorithm for the implementation on current near term quantum devices. In this work, we explore the implementation of VQE on Qiskit for calculating the ground-state energy of diatomic Hydrogen molecule.

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11

Handy, Carlos R. "Orthonormal polynomial projection quantization: an algebraic eigenenergy bounding method." Acta Polytechnica 62, no. 1 (February 28, 2022): 63–79. http://dx.doi.org/10.14311/ap.2022.62.0063.

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The ability to generate tight eigenenergy bounds for low dimension bosonic or ferminonic, hermitian or non-hermitian, Schrödinger operator problems is an important objective in the computation of quantum systems. Very few methods can simultaneously generate lower and upper bounds. One of these is the Eigenvalue Moment Method (EMM) originally introduced by Handy and Besssis, exploiting the use of semidefinite programming/nonlinear-convex optimization (SDP) techniques as applied to the positivity properties of the multidimensional bosonic ground state for a large class of important physical systems (i.e. those admitting a moments’ representation). A recent breakthrough has been achieved through another, simpler, moment representation based quantization formalism, the Orthonormal Polynomial Projection Quantization Bounding Method (OPPQ-BM). It is purely algebraic and does not require any SDP analysis. We discuss its essential structure in the context of several one dimensional examples.

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12

Katayama, Haruna, Noriyuki Hatakenaka, and Ken-ichi Matsuda. "Analogue Hawking Radiation in Nonlinear LC Transmission Lines." Universe 7, no. 9 (September 8, 2021): 334. http://dx.doi.org/10.3390/universe7090334.

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Analogue systems are used to test Hawking radiation, which is hard to observe in actual black holes. One such system is the electrical transmission line, but it suffers the inevitable issue of excess heat that collapses the successfully generated analogue black holes. Soliton provides a possible solution to this problem due to its stable propagation without unnecessary energy dissipation in nonlinear transmission lines. In this work, we propose analogue Hawking radiation in a nonlinear LC transmission line including nonlinear capacitors with a third-order nonlinearity in voltage. We show that this line supports voltage soliton that obeys the nonlinear Schrödinger equation by using the discrete reductive perturbation method. The voltage soliton spatially modifies the velocity of the electromagnetic wave through the Kerr effect, resulting in an event horizon where the velocity of the electromagnetic wave is equal to the soliton velocity. Therefore, Hawking radiation bears soliton characteristics, which significantly contribute to distinguishing it from other radiation.

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13

Al-Jamel, Ahmed. "Heavy quarkonia properties from a hard-wall confinement potential model with conformal symmetry perturbing effects." Modern Physics Letters A 34, no. 37 (December 6, 2019): 1950307. http://dx.doi.org/10.1142/s0217732319503073.

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Heavy [Formula: see text] and [Formula: see text] quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent — with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov–Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization, it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status of conformal symmetry in the heavy flavor sector. The resulting predictions on heavy quarkonia mass spectra and root mean square radii are compared with the available experimental data, as well as with predictions by other theoretical approaches. We observe that a relatively small conformal symmetry perturbing term in the potential suffices to achieve good agreement with data.

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14

Zhong, Xuexiu, and Wenming Zou. "Critical Schrödinger systems in $\mathbb R^N$ with indefinite weight and Hardy potential." Differential and Integral Equations 28, no. 1/2 (January 1, 2015). http://dx.doi.org/10.57262/die/1418310424.

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15

Chen, Xi, Ze Wu, Min Jiang, Xin-You Lü, Xinhua Peng, and Jiangfeng Du. "Experimental quantum simulation of superradiant phase transition beyond no-go theorem via antisqueezing." Nature Communications 12, no. 1 (November 1, 2021). http://dx.doi.org/10.1038/s41467-021-26573-5.

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AbstractThe superradiant phase transition in thermal equilibrium is a fundamental concept bridging statistical physics and electrodynamics, which has never been observed in real physical systems since the first proposal in the 1970s. The existence of this phase transition in cavity quantum electrodynamics systems is still subject of ongoing debates due to the no-go theorem induced by the so-called A2 term. Moreover, experimental conditions to study this phase transition are hard to achieve with current accessible technology. Based on the platform of nuclear magnetic resonance, here we experimentally simulate the occurrence of an equilibrium superradiant phase transition beyond no-go theorem by introducing the antisqueezing effect. The mechanism relies on that the antisqueezing effect recovers the singularity of the ground state via exponentially enhancing the zero point fluctuation of system. The strongly entangled and squeezed Schrödinger cat states of spins are achieved experimentally in the superradiant phase, which may play an important role in fundamental tests of quantum theory and implementations of quantum metrology.

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16

Lou, S. Y., Xia-zhi Hao, and Man Jia. "Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws." Journal of High Energy Physics 2023, no. 3 (March 2, 2023). http://dx.doi.org/10.1007/jhep03(2023)018.

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Abstract Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied to Lax pairs and higher order flows. In other words, if the original lower dimensional model is Lax integrable (possesses Lax pairs) and symmetry integrable (possesses infinitely many higher order symmetries and/or infinitely many conservation laws), then the deformed higher order systems are also Lax integrable and symmetry integrable. For concreteness, the deformation algorithm is applied to the usual (1 + 1)-dimensional Korteweg-de Vries (KdV) equation and the (1 + 1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) system (including nonlinear Schrödinger (NLS) equation as a special example). It is interesting that the deformed (3+1)-dimensional KdV equation is also an extension of the (1 + 1)-dimensional Harry-Dym (HD) type equations which are reciprocal links of the (1+1)-dimensional KdV equation. The Lax pairs of the (3 + 1)-dimensional KdV-HD system and the (2 + 1)-dimensional AKNS system are explicitly given. The higher order symmetries, i.e., the whole (3 + 1)-dimensional KdV-HD hierarchy, are also explicitly obtained via the deformation algorithm. The single soliton solution of the (3 + 1)-dimensional KdV-HD equation is implicitly given. Because of the effects of the deformation, the symmetric soliton shape of the usual KdV equation is no longer conserved and deformed to be asymmetric and/or multi-valued. The deformation conjecture holds for all the known (1 +1)-dimensional integrable local evolution systems that have been checked, and we have not yet found any counter-example so far. The introduction of a large number of (D + 1)-dimensional integrable systems of this paper explores a serious challenge to all mathematicians and theoretical physicists because the traditional methods are no longer directly valid to solve these integrable equations.

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