We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate represe...Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.展开更多
In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it...In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.展开更多
In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product o...In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.展开更多
To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of...To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schroedinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.展开更多
We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy...We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical(QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory,and(2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects(KIEs).In this approach,which is called the PI-FEP/UM method,a light(heavy) isotope is mutated into a heavy(light) counterpart in centroid path integral simulations.The method is illustrated in the study of primary and secondary KIEs in two enzyme systems.In the case of nitroalkane oxidase,the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water.In the dopa delarboxylase reaction,there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions.These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions.展开更多
In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic ord...In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lameUar phase (LAM) region, bicontinuous microemulsion (BμE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers φn, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the B,uE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends.展开更多
文摘We establish the path integral formalism for nondegenerate parametric amplifiers in the entangled state representations. Its advantage in obtaining the energy level gap of this system is analyzed.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and the National Natural Science Foundation of China under Grant No. 10574060
文摘Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.
基金Supported by the National Natural Science Foundation of China under Grant No.10874174 the Specialized Reserach Fund for The Doctoral Progress of Higher Education of China under Grant No.20070358009
文摘In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102,10871135,11031005,11075014
文摘In this paper,we investigate the categorical description of the boson oscillator.Based on the categories constructed by Khovanov,we introduce a categorification of the Fock states and the corresponding inner product of these states.We find that there are two different categorical definitions of the inner product of the Fock states.These two definitions are consistent with each other,and the decategorification results also coincide with those in conventional quantum mechanics.We also find that there are some interesting properties of the 2-morphisms which relate to the inner product of the states.
文摘To describe the physical reality, there are two ways of constructing the dynamical equation of field, differential formalism and integral formalism. The importance of this fact is firstly emphasized by Yang in case of gauge field [Phys. Rev. Lett. 33 (1974) 44fi], where the fact has given rise to a deeper understanding for Aharonov-Bohm phase and magnetic monopole [Phys. Rev. D 12 (1975) 3846]. In this paper we shall point out that such a fact also holds in general wave function of matter, it may give rise to a deeper understanding for Berry phase. Most importantly, we shall prove a point that, for general wave function of matter, in the adiabatic limit, there is an intrinsic difference between its integral formalism and differential formalism. It is neglect of this difference that leads to an inconsistency of quantum adiabatic theorem pointed out by Marzlin and Sanders [Phys. Rev. Lett. 93 (2004) 160408]. It has been widely accepted that there is no physical difference of using differential operator or integral operator to construct the dynamical equation of field. Nevertheless, our study shows that the Schroedinger differential equation (i.e., differential formalism for wave function) shall lead to vanishing Berry phase and that the Schroedinger integral equation (i.e., integral formalism for wave function), in the adiabatic limit, can satisfactorily give the Berry phase. Therefore, we reach a conclusion: There are two ways of describing physical reality, differential formalism and integral formalism; but the integral formalism is a unique way of complete description.
基金supported in part by the National Institutes of Health (GM46736)
文摘We describe a computational approach,incorporating quantum mechanics into enzyme kinetics modeling with a special emphasis on computation of kinetic isotope effects.Two aspects are highlighted:(1) the potential energy surface is represented by a combined quantum mechanical and molecular mechanical(QM/MM) potential in which the bond forming and breaking processes are modeled by electronic structure theory,and(2) a free energy perturbation method in path integral simulation is used to determine both kinetic isotope effects(KIEs).In this approach,which is called the PI-FEP/UM method,a light(heavy) isotope is mutated into a heavy(light) counterpart in centroid path integral simulations.The method is illustrated in the study of primary and secondary KIEs in two enzyme systems.In the case of nitroalkane oxidase,the enzymatic reaction exhibits enhanced quantum tunneling over that of the uncatalyzed process in water.In the dopa delarboxylase reaction,there appears to be distinguishable primary carbon-13 and secondary deuterium KIEs when the internal proton tautomerism is in the N-protonated or in the O-protonated positions.These examples show that the incorporation of quantum mechanical effects in enzyme kinetics modeling offers an opportunity to accurately and reliably model the mechanisms and free energies of enzymatic reactions.
基金supported by the National Natural Science Foundation of China(21174154,20874110,50930002)
文摘In this paper, the phase behavior and interracial properties of symmetric ternary polymeric blends A/B/AB are studied by dissipative particle dynamics (DPD) simulations. By using the structure factor and nematic order parameter, we carefully characterized the diversified phases and phase transitions, and established the phase diagram of such symmetric ternary blends. It can be generally divided into four regions: disordered phase (DIS) region at high temperature, ordered lameUar phase (LAM) region, bicontinuous microemulsion (BμE) channel and phase-separated phase (2P) region at low temperature with the increase of the total volume fractions of homopolymers φn, which shows good accordance with that in previous experimental and theoretical reports. Furthermore, we calculated the elastic constants of 2P and LAM phase, and discussed the transition mechanisms from 2P and LAM to BμE phase, respectively. The results show a direct relevance between the phase transitions and the change of interfacial properties. Finally, we also demonstrate that the B,uE channel becomes narrower in lower temperature caused by the temperature dependence of interfacial properties of ternary blends.