The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the mod...The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.展开更多
The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamenta...The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.展开更多
The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied...The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.展开更多
Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in ...Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.展开更多
This report describes a fundamental model of a quantum circuit for finding complex eigenvalues of Hamiltonian matrices on the quantum computers through the use of an iteration algorithm for estimation of the phase. In...This report describes a fundamental model of a quantum circuit for finding complex eigenvalues of Hamiltonian matrices on the quantum computers through the use of an iteration algorithm for estimation of the phase. In addition to this, we demonstrate the use of the model for simulating the resonant states for quantum systems.展开更多
This report presents a second version of the Interactive Quantum Development Environment (IQDE), virtualized parallel simulation platform for optimized testing of quantum software. IQDE is an interactive quantum simul...This report presents a second version of the Interactive Quantum Development Environment (IQDE), virtualized parallel simulation platform for optimized testing of quantum software. IQDE is an interactive quantum simulator intended for implementation of a classical computer that can simulate numerous controlled and time-dependent operations. The research presents different relations between the operations that can be typically simulated. The virtualized simulation platform carries out numerous single-node and multi-node optimizations, including vectorization, parallelization, cache sharing, as well as overlapping of the computations with the communication. A common strategy for modeling for shared memory is implemented, as well as realistic parallel simulation with cluster management of the parallelization. А detailed analysis of the implementation is performed in order to be demonstrated that the simulator achieves good operation and high efficiency of the hardware, which is only limited by the available memory and the bandwidth of the machine.展开更多
基金Supported by the China Scholarship Councilthe Hanjiang Scholar Project of Shaanxi University of Technology
文摘The equation governing the motion of a quantum particle is considered in nonrelativistic non-commutative phase space. For this aim, we first study new Poisson brackets in non-commutative phase space and obtain the modified equations of motion. Next, using novel transformations, we solve the equation of motion and report the exact analytical solutions.
文摘The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.
文摘The two dimensional quantum dipole springs in background uniform electric and magnetic fields are first studied in the conventional commutative coordinate space, leading to rigorous results. Then, the model is studied in the framework of the noncommutative (NC) phase space. The NC Hamiltonian and angular momentum do not commute any more in this space. By the means of the su(1,1) symmetry and the similarity transformation, exact solutions are obtained for both the NC angular momentum and the NC Hamiltonian.
文摘Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.
文摘This report describes a fundamental model of a quantum circuit for finding complex eigenvalues of Hamiltonian matrices on the quantum computers through the use of an iteration algorithm for estimation of the phase. In addition to this, we demonstrate the use of the model for simulating the resonant states for quantum systems.
文摘This report presents a second version of the Interactive Quantum Development Environment (IQDE), virtualized parallel simulation platform for optimized testing of quantum software. IQDE is an interactive quantum simulator intended for implementation of a classical computer that can simulate numerous controlled and time-dependent operations. The research presents different relations between the operations that can be typically simulated. The virtualized simulation platform carries out numerous single-node and multi-node optimizations, including vectorization, parallelization, cache sharing, as well as overlapping of the computations with the communication. A common strategy for modeling for shared memory is implemented, as well as realistic parallel simulation with cluster management of the parallelization. А detailed analysis of the implementation is performed in order to be demonstrated that the simulator achieves good operation and high efficiency of the hardware, which is only limited by the available memory and the bandwidth of the machine.
