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Volumn 83, Issue 2, 2011, Pages

Escape behavior of quantum two-particle systems with Coulomb interactions

Author keywords

[No Author keywords available]

Indexed keywords

ESCAPE BEHAVIOR; FREE PARTICLES; FUNCTION OF TIME; IDENTICAL PARTICLES; INITIAL ENERGY; PAULI EXCLUSION PRINCIPLE; QUANTUM EFFECTS; SEMI-INFINITE LEADS; SURVIVAL PROBABILITIES; TWO PARTICLES; TWO-PARTICLE SYSTEMS;

EID: 79952558397     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.83.026208     Document Type: Article
Times cited : (37)

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    • Exactly speaking, for example, the plus sign in the plus or minus sign on the right-hand side of Eq. (2) can be taken even for fermions if the wave function is represented as a multiplication of a spatially dependent part and a spin-dependent part, and its spin-dependent part is antisymmetric for exchange of any two particles. However, in this paper we do not consider such a spin effect
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    • The term "survival probability" has been used in some reports, such as Refs. [18-20] and [30] and comes from the fact that P(t) is the probability that particles will "survive" within the subspace at time t. However, it should also be noted that in some papers, like Refs. [6] and [25-27], a quantity like Eq. (3) is called the "nonescape probability," and the term survival probability is used for a slightly different quantity
    • The term "survival probability" has been used in some reports, such as Refs. [18-20] and [30] and comes from the fact that P (t) is the probability that particles will "survive" within the subspace at time t. However, it should also be noted that in some papers, like Refs. [6] and [25-27], a quantity like Eq.\ (3) is called the "nonescape probability," and the term survival probability is used for a slightly different quantity.
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    • 2=x for the two particles in these sums is taken as its half, so that relation (15) is still satisfied even in this spatially discretized case. We also note that the distributions fn(R)(x,t) and fn(L)(x,t) defined by Eqs. (13) and (14), are normalized as ∫0+∞dx fn(R)(x,t)=∫0+∞dx fn(L)(x,t)=1/2.
    • 2 = x for the two particles in these sums is taken as its half, so that relation (15) is still satisfied even in this spatially discretized case. We also note that the distributions f n (R) (x, t) and f n (L) (x, t) defined by Eqs. (13) and (14), are normalized as 0 + ∞ dx f n (R) (x, t) = J 0 + ∞ dx f n (L) (x, t) = 1 / 2.
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