Download - Neue Wege in der Teilchendetektion
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Disordered Solids
real crystals
glasses
spin glass
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Tunneling of Atoms in Solids
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Tunneln
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KCl:Li Specific Heat
specific heat roughly a factor of 10 higher at 0.5 K
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K+ Cl-
Li-Tunneling Systems in KCl-Crystals
Li+ substitutes K+
ionic radius:
8 off-center positions in ⟨111⟩ direction
(100)-plane tunnel splitting:
Li+
with
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Isotope effect
Schottky-Anomaly
number density
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Dielectric Susceptibility
number denstiy
dipole moment
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Thermal Conductivity of KCl:Li Isotope effect
l = 4 mm
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KCl:Li Specific Heat, Concentration Dependence
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Dielectric Susceptibility, Concentration Dependence
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Interacting Tunneling Systems
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Transition to Incoherent Tunneling
defects in crystals: at high concentrations cross over to incoherent tunneling consequences: reduced resonant contribution new phononless relaxation channel incoherent tunneling in glasses at very low temperatures?
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Atomic Tunneling Systems in Glasses
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Atomic Tunneling Systems in Glasses
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Specific Heat
broad distribution of low-energy excitations
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Thermal Conductivity
strong coupling to phonons
systems are localized
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Universality
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Atomic Tunneling Systems in Glasses
energy splitting
distribution function
tunnel splitting
elastic, dielectric und thermal properities
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Thermal Properties in the Tunneling Modell
Spezifische Wärme:
Wärmeleitung:
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Elastic and Dielectric Properties
resonant processes
relaxational processes
modulation of ∆
T < 1 K one-phonon relaxation wide distribution even for fixed E
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Heat Release
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Sound Velocity and Internal Friction
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2 cm
torsion bending torsion
M. Heitz 2000
1 µm silver film
SEM picture
good thermalization
laser-cut glass neck
Elastic Measurements with Mechanical Oscillators
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Sound Velocity
discrepancy at low temperatures
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Internal Friction
T < 30 mK
additional relaxation channel
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Dielectric Constant
inversion symmetry of glasses
no linear terms !
Naughton et al. (4.2 K, 16 T)
Wiegers et al. (2 mK, 9 T)
E polar vector, B axial vector
– Magnetic Field Independent?
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Dielectric Constant at Ultra-low Temperatures
20 µT
B = 0.1 T δε/ε ≈ 0.01
dielectric constant follows field variations extremely high sensitivity to magnetic fields
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Temperature Dependence
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Coherent Properties
two-pulse polarization echoes:
microwave cavity
1 GHz
coherent regime
Rabi frequency 1 GHz 50 mK
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Echo ―Theoretical Background I
coherent regime:
two level approximation:
applied field:
Schrödinger equation:
ansatz:
Rabi frequency:
mit
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Echo ―Theoretical Background II
Bloch equations:
τ1: energy relaxation
τ2: phase coherence time τ1 processes spectral diffusion spin diffusion
T < 1 K one phonon prozess
..... ?
..... ?
polarisation vector:
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Two Pulse Echo I
polarization vector
rotating frame
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Spectral Diffusion
short time limit (no flip limit):
Gaussian decay
long time limit (multiple flip limit):
exponential decay
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Temperature Dependence
short time limit (no flip limit):
long time limit (multiple flip limit):
P. Hu, S.R. Hartmann, PRB 9, 1 (1974) J.L. Black, B.I. Halperin, PRB 16, 2879 (1976) P. Hu, L.R. Walker, PRB 18, 1300 (1978) R. Maynard, R. Rammal, R. Suchail, J. Phys. Paris Lett. 41, L-291 (1980) B.D. Laikhtman, PRB 31, 400 (1985) Yu.M. Galperin, V.L. Gurevich, D.A. Parshin, PRB 37, 10339 (1988)
Theoretical papers:
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Echo Amplitude: Magnetic Field Dependence
Tunneling systems couple to magnetic fields
What is different in case of a-SiO2?
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Nuclear Quadrupole Moment is Important
nuclear quadrupole moment of tunneling particle sees the electric field gradient in the two wells splitting of tunneling levels multi-level systems
magnetic field causes an additional Zeeman splitting of nuclear levels
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hydrogen
Glycerol
proof of the quadrupole model
deuterium atom
D C C C D
D D D
OD OD OD H C C C H
H H H
OH OH OH
Isotope Effect H D
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Evidence for a Dipole Gap in Glasses
modification of density of states: dipole gap slow sweep experiment
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Memory Effect
dielectric constant remembers previous dc-field
slow sweep after applying 5 MV/m for 2 h
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