405 research outputs found
Scaling Limits for the System of Semi-Relativistic Particles Coupled to a Scalar Bose Field
In this paper the Hamiltonian for the system of semi-relativistic particles
interacting with a scalar bose field is investigated. A scaled total
Hamiltonian of the system is defined and its scaling limit is considered. Then
the semi-relativistic Schrodinger operator with an effective potential is
derived
Kramers degeneracy theorem in nonrelativistic QED
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is
proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed
total momentum is also investigated.Comment: LaTex, 11 page
Quantum information with Gaussian states
Quantum optical Gaussian states are a type of important robust quantum states
which are manipulatable by the existing technologies. So far, most of the
important quantum information experiments are done with such states, including
bright Gaussian light and weak Gaussian light. Extending the existing results
of quantum information with discrete quantum states to the case of continuous
variable quantum states is an interesting theoretical job. The quantum Gaussian
states play a central role in such a case. We review the properties and
applications of Gaussian states in quantum information with emphasis on the
fundamental concepts, the calculation techniques and the effects of
imperfections of the real-life experimental setups.
Topics here include the elementary properties of Gaussian states and relevant
quantum information device, entanglement-based quantum tasks such as quantum
teleportation, quantum cryptography with weak and strong Gaussian states and
the quantum channel capacity, mathematical theory of quantum entanglement and
state estimation for Gaussian states.Comment: 170 pages. Minors of the published version are corrected and listed
in the Acknowledgement part of this versio
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a
spin-1/2 electron in the standard model of non-relativistic QED. We study the
Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum.
For small enough values of the fine-structure constant, we prove that the
ground state is unique. This result reflects the hyperfine structure of the
hydrogen atom ground state.Comment: 22 pages, 3 figure
Enhanced binding revisited for a spinless particle in non-relativistic QED
We consider a spinless particle coupled to a quantized Bose field and show
that such a system has a ground state for two classes of short-range potentials
which are alone too weak to have a zero-energy resonance
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
Binding threshold for the Pauli-Fierz operator
For the Pauli-Fierz operator with a short range potential we study the
binding threshold as a function of the fine structure constant and
show that it converges to the binding threshold for the Schr\"odinger operator
in the small limit
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