5,331 research outputs found
Lattice Magnetic Walks
Sums of walks for charged particles (e.g. Hofstadter electrons) on a square
lattice in the presence of a magnetic field are evaluated. Returning loops are
systematically added to directed paths to obtain the unrestricted propagators.
Expressions are obtained for special values of the magnetic flux-per-plaquette
commensurate with the flux quantum. For commensurate and incommensurate values
of the flux, the addition of small returning loops does not affect the general
features found earlier for directed paths. Lattice Green's functions are also
obtained for staggered flux configurations encountered in models of high-Tc
superconductors.Comment: 31 pages, Plain TeX, 2 figures (available upon request),
UR-CM-93-10-1
Nucleon structure functions with domain wall fermions
We present a quenched lattice QCD calculation of the first few moments of the
polarized and un-polarized structure functions of the nucleon. Our calculations
are done using domain wall fermions and the DBW2 gauge action with inverse
lattice spacing ~1.3GeV, physical volume approximatelly (2.4 fm)^3, and light
quark masses down to about 1/4 the strange quark mass. Values of the individual
moments are found to be significantly larger than experiment, as in past
lattice calculations, but interestingly the chiral symmetry of domain wall
fermions allows for a precise determination of the ratio of the flavor
non-singlet momentum fraction to the helicity distribution, which is in very
good agreement with experiment. We discuss the implications of this result.
Next, we show that the chiral symmetry of domain wall fermions is useful in
eliminating mixing of power divergent lower dimensional operators with twist-3
operators. Finally, we find the isovector tensor charge at renormalization
scale 2 GeV in the MS bar scheme to be 1.192(30), where the error is the
statistical error only.Comment: 41 pages, 17 figure
Looking for ultralight dark matter near supermassive black holes
Measurements of the dynamical environment of supermassive black holes (SMBHs)
are becoming abundant and precise. We use such measurements to look for
ultralight dark matter (ULDM), which is predicted to form dense cores
("solitons") in the centre of galactic halos. We search for the gravitational
imprint of an ULDM soliton on stellar orbits near Sgr A* and by combining
stellar velocity measurements with Event Horizon Telescope imaging of M87*.
Finding no positive evidence, we set limits on the soliton mass for different
values of the ULDM particle mass . The constraints we derive exclude the
solitons predicted by a naive extrapolation of the soliton-halo relation, found
in DM-only numerical simulations, for (from Sgr A*) and
(from M87*). However, we present
theoretical arguments suggesting that an extrapolation of the soliton-halo
relation may not be adequate: in some regions of the parameter space, the
dynamical effect of the SMBH could cause this extrapolation to over-predict the
soliton mass by orders of magnitude.Comment: 9 pages + appendices, 5 + 2 figures. v2: some clarifications and
references added; conclusions unchanged; version published in JCAP. v3: few
typos correcte
Modular Exponentiation on Reconfigurable Hardware
It is widely recognized that security issues will play a crucial role in the majority of future computer and communication systems. A central tool for achieving system security are cryptographic algorithms. For performance as well as for physical security reasons, it is often advantageous to realize cryptographic algorithms in hardware. In order to overcome the well-known drawback of reduced flexibility that is associated with traditional ASIC solutions, this contribution proposes arithmetic architectures which are optimized for modern field programmable gate arrays (FPGAs). The proposed architectures perform modular exponentiation with very long integers. This operation is at the heart of many practical public-key algorithms such as RSA and discrete logarithm schemes. We combine two versions of Montgomery modular multiplication algorithm with new systolic array designs which are well suited for FPGA realizations. The first one is based on a radix of two and is capable of processing a variable number of bits per array cell leading to a low cost design. The second design uses a radix of sixteen, resulting in a speed-up of a factor three at the cost of more used resources. The designs are flexible, allowing any choice of operand and modulus. Unlike previous approaches, we systematically implement and compare several versions of our new architecture for different bit lengths. We provide absolute area and timing measures for each architecture on Xilinx XC4000 series FPGAs. As a first practical result we show that it is possible to implement modular exponentiation at secure bit lengths on a single commercially available FPGA. Secondly we present faster processing times than previously reported. The Diffie-Hellman key exchange scheme with a modulus of 1024 bits and an exponent of 160 bits is computed in 1.9 ms. Our fastest design computes a 1024 bit RSA decryption in 3.1 ms when the Chinese remainder theorem is applied. These times are more than ten times faster than any reported software implementation. They also outperform most of the hardware-implementations presented in technical literature
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