Calculating the linear response functions of noninteracting electrons with a time-dependent Schrödinger equation

Iitaka, Toshiaki; Nomura, Shintaro; Hasegawa, Hideki; Zhao, Xinwei; Aoyagi, Yoshinobu; Sugano, Takuo

doi:10.1103/physreve.56.1222

Cited by 79 publications

(83 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our simulations we use the spin-up-spin-down basis and use units such thath = 1 (hence, all quantities are dimensionless). Numerically, the real-time propagation by e −itH is carried out by means of the Chebyshev polynomial algorithm [22][23][24][25], thereby solving the TDSE for the whole system starting from the initial state | (0) . This algorithm yields results that are very accurate (close to machine precision), independent of the time step used [18].…”

Section: A Time Evolutionmentioning

confidence: 99%

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

et al. 2013

View full text Add to dashboard Cite

We consider the decoherence of a quantum system S coupled to a quantum environment E. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system S + E we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of S as a function of the size D E of the Hilbert space of E. This sum decreases as 1/ √ D E as long as D E 1. We test this scaling prediction by performing large-scale simulations which solve the time-dependent Schrödinger equation for a ring of spin-1/2 particles, four of them belonging to S and the others to E, and for this ring with small world bonds added in E and/or between S and E. The spin-1/2 particles experience nearest-neighbor interactions that are identical for the interactions within S and random for the interactions within E and between S and E, or that are all identical. Provided that the time evolution drives the whole system from the initial state toward a scaling state, a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. We examine various interaction parameters and initial states for our model system to find whether or not the time evolution reaches the class of states that have the scaling property. For the homogeneous ring we find that the evolution for select initial states does not reach these scaling states. This conclusion is not modified if we add some homogeneous random connections. For a ring we find that some randomness in the interaction parameters is required so that most initial configurations are driven toward the scaling state. Furthermore, if the amount of randomness is small the time required to reach the scaling states may be very large. For the case of all random interactions in E the ring is driven toward the scaling state. Adding small world bonds between S and E with random interaction strengths may decrease the time required to reach the scaling state or may prevent the scaling state from being reached. For the latter case we show that increasing the complexity of the environment by adding extra connections within the environment suffices to observe the predicted scaling behavior.

show abstract

Section: A Time Evolutionmentioning

confidence: 99%

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

et al. 2013

View full text Add to dashboard Cite

show abstract

“…The numerical solution of the TDSE is performed by the Chebyshev polynomial algorithm, which is known to be extremely accurate independent of the time step used. [15][16][17][18] We adopt open boundary conditions, not periodic boundary conditions, because the periodic boundary condition would introduce two DWs in the initial state. In this paper, we display the results at time intervals of = /5J and use units such that ប = 1 and J =1.…”

Section: Dynamically Stable Domain Wallsmentioning

confidence: 99%

Domain-wall dynamics near a quantum critical point

2007

View full text Add to dashboard Cite

show abstract

“…(2) looks very similar to that of the linearresponse function, and that, therefore, we may calculate χ (3) by using the linear-scaling time-dependent method for the linear-response functions [7,8],…”

Section: Tpa Coefficientmentioning

confidence: 99%

“…In this paper, we develop a new algorithm for calculating TPA spectra by using semiempirical local pseudopotentials [3], finite difference method in real space [4], and a linearscaling time-dependent method which has been applied to the calculation of the linearresponse functions [5,6,7,8]. This efficient algorithm made it possible, for the first time, to calculate the size effect on the TPA spectra of very large nanocrystallites without using effective-mass approximation.…”

Section: Introductionmentioning

confidence: 99%