This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the prop...This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.展开更多
The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstat...The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.展开更多
For classical transformation (q1,q2) → (Aq1 + Bq2, Cq1 + Dq2), where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix (A B C D ). The explicit operators L, D, and U ...For classical transformation (q1,q2) → (Aq1 + Bq2, Cq1 + Dq2), where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix (A B C D ). The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.展开更多
We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode rep...We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.展开更多
In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schroedinger's picture of quantum dynamics. Here it is shown in both cases how to ma...In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schroedinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators. These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.展开更多
We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is s...We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e+e-→μ+μ- and QED one-loop vacuum polarization of photon.展开更多
The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and bio...The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ|μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins (MAP) that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer's disease.展开更多
文摘This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.
文摘The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.
基金Supported by the President Foundation of Chinese Academy of Science and Specialized Research Fund for the Doctorial Progress of Higher Education under Grant No.20070358009
文摘For classical transformation (q1,q2) → (Aq1 + Bq2, Cq1 + Dq2), where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix (A B C D ). The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.
基金supported by the National Natural Science Foundation of China through the Project "Science Center for Luminescence from Molecular Aggregates(SCELMA)" (No.21788102)the Ministry of Science and Technology of China through the National Key R&D Plan (No.2017YFA0204501)supported by the National Natural Science Foundation of China (No.22003029)
文摘We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.
基金Supported by the National Research Foundation of South Africa
文摘In principle, non-Hermitian quantum equations of motion can be formulated using as a starting point either the Heisenberg's or the Schroedinger's picture of quantum dynamics. Here it is shown in both cases how to map the algebra of commutators, defining the time evolution in terms of a non-Hermitian Hamiltonian, onto a non-Hamiltonian algebra with a Hermitian Hamiltonian. The logic behind such a derivation is reversible, so that any Hermitian Hamiltonian can be used in the formulation of non-Hermitian dynamics through a suitable algebra of generalized (non-Hamiltonian) commutators. These results provide a general structure (a template) for non-Hermitian equations of motion to be used in the computer simulation of open quantum systems dynamics.
基金Supported by National Natural Science Foundation of China under Grant No. 10475103
文摘We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e+e-→μ+μ- and QED one-loop vacuum polarization of photon.
文摘The relation between microtubules architecture in the cytoskeletal structure inside the dendrites and soma and the emergence of neuron function and firing action potential crosses the tiny line between physics and biology. As decoherence is a fundamental mechanism in some biological process such as photosynthesis and others examples, the gravitational quantum approach may contribute to elucidate if neuron function really emerges from quantum coherence in neuronal microtubules. The Einstein equation correlates the stress-energy tensor Tμv to a specific divergence-free combination Ricci tensor Rμv and the metric. In the semiclassical formulation, we have Gμv = Rμv -1/2gμvR=8πG/C^4〈ψ|μvψ〉 which describes the quantum field in curved space-time geometry. But for a more precise equation in relation to the stress-energy tensor, we know that in a non-zero temperature, the wave-function is not enough to describe the physical reality. A more precise equation demands a formulation in the density-matrix form but for now there is no Diosi-Penrose model with density-matrix formulation. Such a density-matrix description can be viewed as a probability mixture of different wave-functions. Using some algebra and rules related to the mathematical manipulation of the density-matrix applied to operators, such the stress energy tensor, we found the von Neumann-Einstein equation for the general relativity equation in the density matrix operator form, Gμv = 8πG/C^4Tr[pTμv]. Thus density-matrix operator--instead of just a wave function of pure states--applied to the stress-energy tensor gives the curvature of space time, given by Einstein tensor, Gμv. The quantum fluctuation in the gravitational space-time field might feed back to decohere the quantum density-matrix. As long as decoherence can be viewed as the loss of information from a system to the environment, the density-matrix p is also related to that process and considering the measurement problem, density-matrix /garter is a more complete description of the possible outcome of the measurement. It is possible that some characteristics of the special microtubulin-associated proteins (MAP) that capes the dendritic-somatic microtubulins which could induces longer-lived nuclear spin states prevented from de-polymerization and suitable for long term information encode and memory. Understand the mechanism by which the hyper-phosphorylation in type tau-MAP displacements from microtubulins results in neurofibrillary tangles and cognitive dysfunctions in Alzheimer's disease.