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Ground states of coupled critical Choquard equations with weighted potentials

Zhu Gaili, Duan Chunping, Zhang Jianjun, Zhang Huixing

Opuscula Mathematica

2022

Vol. 42, no. 2

337--354

In this paper, we are concerned with the following coupled Choquard type system with weighted potentials [formula] where N ≥ 3, μ1, μ2, β > 0 and V1(x), V2(x) are nonnegative functions. Via the variational approach, one positive ground state solution of this system is obtained under some certain assumptions on V1(x), V2(x) and Q(x). Moreover, by using Hardy’s inequality and one Pohozǎev identity, a non-existence result of non-trivial solutions is also considered.

Ground states for fractional nonlocal equations with logarithmic nonlinearity

Guo Lifeng, Sun Yan, Shi Guannan

Opuscula Mathematica

2022

Vol. 42, no. 2

157--178

In this paper, we study on the fractional nonlocal equation with the logarithmic nonlinearity formed by [formula] where 2 < q < 2∗s, LK is a non-local operator, Ω is an open bounded set of Rn with Lipschitz boundary. By using the fractional logarithmic Sobolev inequality and the linking theorem, we present the existence theorem of the ground state solutions for this nonlocal problem.

Time evolution of the haldane state after a quantum quench

Woźniak D., Drzewiński A., Kamieniarz G.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

151--156

In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified. The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been investigated.