998 research outputs found
The Solution of the Relativistic Schrodinger Equation for the -Function Potential in 1-dimension Using Cutoff Regularization
We study the relativistic version of Schr\"odinger equation for a point
particle in 1-d with potential of the first derivative of the delta function.
The momentum cutoff regularization is used to study the bound state and
scattering states. The initial calculations show that the reciprocal of the
bare coupling constant is ultra-violet divergent, and the resultant expression
cannot be renormalized in the usual sense. Therefore a general procedure has
been developed to derive different physical properties of the system. The
procedure is used first on the non-relativistic case for the purpose of
clarification and comparisons. The results from the relativistic case show that
this system behaves exactly like the delta function potential, which means it
also shares the same features with quantum field theories, like being
asymptotically free, and in the massless limit, it undergoes dimensional
transmutation and it possesses an infrared conformal fixed point.Comment: 32 pages, 5 figure
March CRF: an Efficient Test for Complex Read Faults in SRAM Memories
In this paper we study Complex Read Faults in SRAMs, a combination of various malfunctions that affect the read operation in nanoscale memories. All the memory elements involved in the read operation are studied, underlining the causes of the realistic faults concerning this operation. The requirements to cover these fault models are given. We show that the different causes of read failure are independent and may coexist in nanoscale SRAMs, summing their effects and provoking Complex Read Faults, CRFs. We show that the test methodology to cover this new read faults consists in test patterns that match the requirements to cover all the different simple read fault models. We propose a low complexity (?2N) test, March CRF, that covers effectively all the realistic Complex Read Fault
Self-adjoint Extensions for Confined Electrons:from a Particle in a Spherical Cavity to the Hydrogen Atom in a Sphere and on a Cone
In a recent study of the self-adjoint extensions of the Hamiltonian of a
particle confined to a finite region of space, in which we generalized the
Heisenberg uncertainty relation to a finite volume, we encountered bound states
localized at the wall of the cavity. In this paper, we study this situation in
detail both for a free particle and for a hydrogen atom centered in a spherical
cavity. For appropriate values of the self-adjoint extension parameter, the
bound states lo calized at the wall resonate with the standard hydrogen bound
states. We also examine the accidental symmetry generated by the Runge-Lenz
vector, which is explicitly broken in a spherical cavity with general Robin
boundary conditions. However, for specific radii of the confining sphere, a
remnant of the accidental symmetry persists. The same is true for an electron
moving on the surface of a finite circular cone, bound to its tip by a 1/r
potential.Comment: 22 pages, 9 Figure
Variation aware analysis of bridging fault testing
This paper investigates the impact of process variation on test quality with regard to resistive bridging faults. The input logic threshold voltage and gate drive strength parameters are analyzed regarding their process variation induced influence on test quality. The impact of process variation on test quality is studied in terms of test escapes and measured by a robustness metric. It is shown that some bridges are sensitive to process variation in terms of logic behavior, but such variation does not necessarily compromise test quality if the test has high robustness. Experimental results of Monte-Carlo simulation based on recent process variation statistics are presented for ISCAS85 and -89 benchmark circuits, using a 45nm gate library and realistic bridges. The results show that tests generated without consideration of process variation are inadequate in terms of test quality, particularly for small test sets. On the other hand, larger test sets detect more of the logic faults introduced by process variation and have higher test quality
Dynamic and Leakage Power-Composition Profile Driven Co-Synthesis for Energy and Cost Reduction
Recent research has shown that combining dynamic voltage scaling (DVS) and adaptive body bias (ABB) techniques achieve the highest reduction in embedded systems energy dissipation [1]. In this paper we show that it is possible to produce comparable energy saving to that obtained using combined DVS and ABB techniques but with reduced hardware cost achieved by employing processing elements (PEs) with separate DVS or ABB capability. A co-synthesis methodology which is aware of tasks’ power-composition profile (the ratio of the dynamic power to the leakage power) is presented. The methodology selects voltage scaling capabilities (DVS, ABB, or combined DVS and ABB) for the PEs, maps, schedules, and voltage scales applications given as task graphs with timing constraints, aiming to dynamic and leakage energy reduction at low hardware cost. We conduct detailed experiments, including a real-life example, to demonstrate the effectiveness of our methodology. We demonstrate that it is possible to produce designs that contain PEs with only DVS or ABB technique but have energy dissipation that are only 4.4% higher when compared with the same designs that employ PEs with combined DVS and ABB capabilities
Asymptotic Freedom, Dimensional Transmutation, and an Infra-red Conformal Fixed Point for the -Function Potential in 1-dimensional Relativistic Quantum Mechanics
We consider the Schr\"odinger equation for a relativistic point particle in
an external 1-dimensional -function potential. Using dimensional
regularization, we investigate both bound and scattering states, and we obtain
results that are consistent with the abstract mathematical theory of
self-adjoint extensions of the pseudo-differential operator . Interestingly, this relatively simple system is asymptotically free. In
the massless limit, it undergoes dimensional transmutation and it possesses an
infra-red conformal fixed point. Thus it can be used to illustrate non-trivial
concepts of quantum field theory in the simpler framework of relativistic
quantum mechanics
Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity
The non-relativistic hydrogen atom enjoys an accidental symmetry,
that enlarges the rotational symmetry, by extending the angular
momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom
the accidental symmetry is partially lifted. Due to the Johnson-Lippmann
operator, which commutes with the Dirac Hamiltonian, some degeneracy remains.
When the non-relativistic hydrogen atom is put in a spherical cavity of radius
with perfectly reflecting Robin boundary conditions, characterized by a
self-adjoint extension parameter , in general the accidental
symmetry is lifted. However, for (where is the Bohr
radius and is the orbital angular momentum) some degeneracy remains when
or . In the relativistic case, we
consider the most general spherically and parity invariant boundary condition,
which is characterized by a self-adjoint extension parameter. In this case, the
remnant accidental symmetry is always lifted in a finite volume. We also
investigate the accidental symmetry in the context of the Pauli equation, which
sheds light on the proper non-relativistic treatment including spin. In that
case, again some degeneracy remains for specific values of and .Comment: 27 pages, 7 figure
Majorana Fermions in a Box
Majorana fermion dynamics may arise at the edge of Kitaev wires or
superconductors. Alternatively, it can be engineered by using trapped ions or
ultracold atoms in an optical lattice as quantum simulators. This motivates the
theoretical study of Majorana fermions confined to a finite volume, whose
boundary conditions are characterized by self-adjoint extension parameters.
While the boundary conditions for Dirac fermions in -d are characterized
by a 1-parameter family, , of self-adjoint extensions,
for Majorana fermions is restricted to . Based on this result,
we compute the frequency spectrum of Majorana fermions confined to a 1-d
interval. The boundary conditions for Dirac fermions confined to a 3-d region
of space are characterized by a 4-parameter family of self-adjoint extensions,
which is reduced to two distinct 1-parameter families for Majorana fermions. We
also consider the problems related to the quantum mechanical interpretation of
the Majorana equation as a single-particle equation. Furthermore, the equation
is related to a relativistic Schr\"odinger equation that does not suffer from
these problems.Comment: 23 pages, 2 figure
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