2,125 research outputs found

### Regularization, Renormalization and Range: The Nucleon-Nucleon Interaction from Effective Field Theory

Regularization and renormalization is discussed in the context of low-energy
effective field theory treatments of two or more heavy particles (such as
nucleons). It is desirable to regulate the contact interactions from the outset
by treating them as having a finite range. The low energy physical observables
should be insensitive to this range provided that the range is of a similar or
greater scale than that of the interaction. Alternative schemes, such as
dimensional regularization, lead to paradoxical conclusions such as the
impossibility of repulsive interactions for truly low energy effective theories
where all of the exchange particles are integrated out. This difficulty arises
because a nonrelativistic field theory with repulsive contact interactions is
trivial in the sense that the $S$ matrix is unity and the renormalized coupling
constant zero. Possible consequences of low energy attraction are also
discussed. It is argued that in the case of large or small scattering lengths,
the region of validity of effective field theory expansion is much larger if
the contact interactions are given a finite range from the beginning.Comment: 7 page

### Flexible Graphene Transistor Architecture for Optical Sensor Technology.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2017

### The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory

We examine the role of the Delta-Delta intermediate state in low energy NN
scattering using effective field theory. Theories both with and without pions
are discussed. They are regulated with dimensional regularization and MSbar
subtraction. We find that the leading effects of the Delta-Delta state can be
absorbed by a redefinition of the contact terms in a theory with nucleons only.
It does not remove the requirement of a higher dimension operator to reproduce
data out to moderate momentum. The explicit decoupling of the Delta-Delta state
is shown for the theory without pions.Comment: 16 pages, 3 figures, uses harvma

### Bound States and Power Counting in Effective Field Theories

The problem of bound states in effective field theories is studied. A
rescaled version of nonrelativistic effective field theory is formulated which
makes the velocity power counting of operators manifest. Results obtained using
the rescaled theory are compared with known results from NRQCD. The same ideas
are then applied to study Yukawa bound states in 1+1 and 3+1 dimensions, and to
analyze when the Yukawa potential can be replaced by a delta-function
potential. The implications of these results for the study of nucleon-nucleon
scattering in chiral perturbation theory is discussed.Comment: 23 pages, eps figures, uses revte

### Complex collective states in a one-dimensional two-atom system

We consider a pair of identical two-level atoms interacting with a scalar
field in one dimension, separated by a distance $x_{21}$. We restrict our
attention to states where one atom is excited and the other is in the ground
state, in symmetric or anti-symmetric combinations. We obtain exact collective
decaying states, belonging to a complex spectral representation of the
Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and
the real parts give the average energy of the collective states. In one
dimension there is strong interference between the fields emitted by the atoms,
leading to long-range cooperative effects. The decay rates and the energy
oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates
will either decrease, vanish or increase as compared with the one-atom decay
rate. We have sub- and super-radiance at periodic intervals. Our model may be
used to study two-cavity electron wave-guides. The vanishing of the collective
decay rates then suggests the possibility of obtaining stable configurations,
where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.

### Causality, delocalization and positivity of energy

In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at $t = 0$ are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.Comment: 14 pages, 5 figure

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