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11.
The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in
a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using
the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF
av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE
ac with the UHF-energy shows thatE
UHF<E
ac in each case revealing some kind of an upper bound nature ofE
ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is
explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed. 相似文献
12.
An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 相似文献
13.
The properties of the transfer-matrix of U(1) lattice gauge theory in the Fourier basis are explored. Among other statements it is shown: (i) the transfer-matrix is block-diagonal, (ii) all consisting vectors of a block are known based on an arbitrary block vector, (iii) the ground-state belongs to the zero-mode's block. The emergence of maximum-points in matrix-elements as functions of the gauge coupling is clarified. Based on explicit expressions for the matrix-elements we present numerical results as tests of our statements. 相似文献
14.
15.
16.
Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves
a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition
for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization
(one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent
state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution.
Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M
* (M* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find
that: 1) for M
* ≪ M ≪ M
*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t1, t2, t3 and t*; 2) there are transient regimes (t
1 ≲ t ≲ t
3) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter
than t2. The chain growth is auto-accelerated for t
1 ≲ t ≲ t
2 : the cut-off chain length (= polymerization degree 〈n〉w
N
1 ∝ t
2 in this regime. 4) For t
2 < t < t
3 the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N1 is decreasing with time in this regime, while the length scale N2 of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t*, shows a sharp maximum in the vicinity of M*; the effective exponent
is as high as ∼ σ-1/3 just above M*. 相似文献
17.
We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E8 gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT . 相似文献
18.
Sutapa Saha Some Sankar Bhattacharya Tamal Guha Saronath Halder Manik Banik 《Annalen der Physik》2020,532(12):2000334
Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However, a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in “space-like” and/or “time-like” paradigms. In this letter, a communication task involving three spatially separated parties is proposed where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. This task is called authentication with limited communication, the restrictions on communication being: i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several nonclassical theories although they might possess stronger “space-like” and/or “time-like” correlations. Surprisingly, quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other nonclassical strategies. 相似文献
19.
简要介绍现代酸碱理论的建立及其基本概念。现代酸碱理论包括了Brφnsted-Lowry酸碱理论、Lewis酸碱理论、HSAB理论和超酸理论。举例介绍了与物理有机化学、有机合成、有机催化等领域相关的现代酸碱理论的广泛应用。 相似文献
20.
Michael E. Cates tienne Fodor Tomer Markovich Cesare Nardini Elsen Tjhung 《Entropy (Basel, Switzerland)》2022,24(2)
Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself. 相似文献