The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies...The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies a canonical transformation. Using the to describe the system, it is proved that if the Hartrec type approximation is adopted, or the c-number approach is used, the Bogoliubov transformation can be derived via the U-matrix theory if the perturbing Hamiltonian is turned on ’suddenly’. It is also shown that based on the U-matrix, the BCS ground state wave function of a superconducting system can be deduced under the sudden switching condition.展开更多
In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transform...In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.展开更多
We introduce the coordinate-dependent N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standar...We introduce the coordinate-dependent N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. The properties of the corresponding N-mode squeezed states are also discussed.展开更多
文摘The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies a canonical transformation. Using the to describe the system, it is proved that if the Hartrec type approximation is adopted, or the c-number approach is used, the Bogoliubov transformation can be derived via the U-matrix theory if the perturbing Hamiltonian is turned on ’suddenly’. It is also shown that based on the U-matrix, the BCS ground state wave function of a superconducting system can be deduced under the sudden switching condition.
文摘In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.
文摘We introduce the coordinate-dependent N-mode squeezing transformation and show that it cain be constructed by the combination of two unitary transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. The properties of the corresponding N-mode squeezed states are also discussed.
