Terms Of Transition Amplitudes Research Articles

Remote one-qubit-state control using the pure initial state of a two-qubit sender: Selective-region and eigenvalue creation

We study the problem of remote one-qubit mixed state creation using a pure initial state of two-qubit sender and spin-1/2 chain as a connecting line. We express the parameters of creatable states in terms of transition amplitudes. We show that the creation of a complete receiver's state space can be achieved only in the chain engineered for the one-qubit perfect state transfer (PST) (for instance, in the fully engineered Ekert chain); the chain can be arbitrarily long in this case. As for the homogeneous chain, the creatable receiver's state region decreases quickly with the chain length. Both homogeneous chains and chains engineered for PST can be used for the purpose of selective state creation, when only the restricted part of the whole receiver's state space is of interest. Among the parameters of the receiver's state, the eigenvalue is the most hard to create and therefore deserves special study. Regarding the homogeneous spin chain, an arbitrary eigenvalue can be created only if the chain is of no more than 34 nodes. The alternating chain allows us to increase this length to up to 68 nodes.

Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance

We argue that the holographic principle may be hinted at already from low-energy considerations, assuming diffeomorphism invariance, quantum mechanics and Minkowski-like causality. We consider the states of finite spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy regularization is assumed. We note a natural dependence of the Hilbert space on a codimension-2 boundary surface. The Hilbert product is defined dynamically, in terms of transition amplitudes which are described by a path integral. We show that a canonical basis is incompatible with these assumptions, which opens the possibility for a smaller Hilbert-space dimension than canonically expected. We argue further that this dimension may decrease with surface area at constant volume, hinting at holographic area proportionality. We draw comparisons with other approaches and setups, and propose an interpretation for the non-holographic space of graviton states at asymptotically Minkowski null infinity.

MELOSH CONSTRUCTION OF RELATIVISTIC THREE-QUARK BARYON WAVE FUNCTIONS

A method for constructing a complete set of relativistic three-quark states in light front dynamics is implemented for the nucleon, N*(1520) and N*(1535). This approach facilitates constructing states containing virtual antiquarks and a physical interpretation is provided in terms of transition amplitudes from quark to quark–gluon or quark–Goldstone boson Fock states of chiral dynamics generated by flux tube breaking expected in QCD at intermediate distances.

Mixed boundary conditions in quantum field theory

When quantum field theory is formulated in terms of transition amplitudes between initial and final configurations, it is important to impose mathematically consistent boundary conditions on the fields. The choice of boundary conditions is also important when dealing with elliptic complexes and index theorems on bounded manifolds. Although Dirichlet and Neumann boundary conditions are adequate for many purposes, they are not always appropriate. However, a number of the remaining cases can be handled by imposing Dirichlet conditions on certain field components and Neumann conditions on the others. Quantum gravity and supergravity, spinor field theory, and various elliptic complexes all lend themselves to mixed boundary conditions of this sort. The mathematical significance of mixed boundary conditions is investigated, and a simple rule is obtained for determining which field components should obey which boundary conditions. It will be shown that gauge transformations on a bounded manifold give rise to intrinsic gauge transformations within the boundary. This result is used to define gauge-invariant and BRS-invariant quantum amplitudes for boundary configurations. The most general form for mixed boundary conditions on the Dirac operator and the de Rham complex will also be derived.

A semiclassical sudden approximation for rotational excitation

Within the energy-sudden approximation the motion of the target and the projectiles can be decoupled and the transition amplitude for differential inelastic cross sections can be expressed entirely in terms of transition amplitudes involving only orbital quantum numbers. This property naturally lends itself to a purely quantal treatment of the target dynamics and a classical or semiclassical treatment of the relative motion with no further approximation: the point of this separation being that the former usually involves small and the latter large quantum numbers. For rotational excitation of the linear molecules the axial symmetry reduces the problem further to finding a set of one-dimensional transition amplitudes. The authors show how these elements can be combined to produce a simple yet effective and accurate method of obtaining inelastic differential transition amplitudes using only classical trajectories. The method has none of the problems associated with the usual purely classical descriptions; it treats interference effects and tunnelling accurately and handles target quantisation exactly.

Calculation of nuclear-spin-relaxation rate for spin-polarized atomic hydrogen

Approximations introduced in previous calculations of spin relaxation for spin-polarized atomic hydrogen are investigated by carrying out a more exact coupled-channel calculation. With the exception of the high-temperature approximation, the approximations turn out to be justified up to the ${10}^{\ensuremath{-}3}$ level of accuracy. It is shown that at the lowest temperatures for which experimental data are available, the high-temperature limit underestimates relaxation rates by a factor of up to 2. For a comparison with experimental data it is also of interest to pay attention to the expression for the atomic hydrogen relaxation rates in terms of transition amplitudes for two-particle collisions. Discrepancies by a factor of 2 among previous derivations of relaxation rates are pointed out. To shed light on these discrepancies we present two alternative derivations in which special attention is paid to identical-particle aspects. Comparing with experiment, we find our theoretical volume relaxation rate to be in better agreement with measured values than that obtained by other groups. The theoretical surface relaxation rate, however, still shows a discrepancy with experiment by a factor of order 50.

Tables of Auger transition amplitudes

A short review of the theory for the Auger transition in a mixed coupling scheme is given, and an expression for the transition probability in terms of transition amplitudes has been derived. The amplitudes for all Auger transitions in systems with initially filled shells have been calculated and are tabulated in terms of D and E radial integrals.

Effective Schrödinger equations for the elastic interaction of heavy ions

Starting from the many-body Schrödinger equation and using completely antisymmetric state vectors, an effective Hamiltonian formalism is developed which is appropriate for a description of elastic scattering of heavy ions. The additional potential terms arising from the elimination of all non-elastic channels are non-local and non-hermitean. They can be written in terms of transition amplitudes and state densities, so that an approximate evaluation seems possible within the two-center shell model. Special attention is paid to the imaginary part of the potential. Some qualitative features of the imaginary potential are discussed, taking integrals of motion into account. Finally, the possible extension of our treatment to reaction channels is sketched.

Excitations as ground state variational parameters

The ground state density matrix can be expressed in terms of transition amplitudes 〈r|a a + a b| g〉 by the following relation: 〈 g|a a +a ca b +a d|g〉= Σ r 〈 g|a a +a c|r〉〈r|a b +a d| g〉. A formalism is derived in which these transition amplitudes are used as ground state variational p parameters. The quadratic form with transition amplitudes as variational parameters keeps the above matrix non-negative definite. This represents one necessary N-representability condition. This condition plus symmetry and trace relations are used to bound the two-body density matrix. (It keeps also the one-body density matrix between 0 and 1.) the trial ground state is also restricted in such a way that already half of the particle-hole excited states exhausts the sum over r. The variational equations have the form of a secular equation similar to that in the random phase approximation. The single-particle energies are, however, introduced as Lagrange multipliers for the trace relations of the density matrix. The one-body density matrix is also determined using variation methods. Additional Lagrange multipliers are introduced to guarantee certain symmetry relations, which are disregarded in the RPA. The obtained ground state is then consistent with excited states having different quantum numbers. The calculation for a simple system with a schematic intershell pairing is compared with the exact solution, the RPA and some other methods. The ground state energies and transition amplitudes are good for the entire range of the interaction.