PCE STAMP

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PCE STAMP
Physics Astronomy UBC Vancouver
Pacific Institute for Theoretical Physics
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EMERGENCE vs REDUCTIONISM
The reductionist view is that all matter can be
understood in terms of its basic constituents.
It is an atomistic point of view. It is a
programme.
The emergence point of view says that
structures of matter at higher levels, in more
complex systems, CANNOT be
understood in terms of basic constituents- that
they have ineluctably complex properties, not
understandable in terms of elementary
constituents, even in principle. This is also a
programme.
NB1 Many if not most emergence believers still
nevertheless assume that matter is composed of
bits (the lego philosophy, or soft
emergence)
NB2 Some argue there is no end in sight to the
long road towards elementary constituents, in
particle physics. Nature may just be wheels
within wheels.. (ie. an unending series of
effective Hamiltonians).
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Hard Soft EMERGENCE
The House is built of bricks, glass, metal,
etc.-with a sufficiently detailed blueprint, one
could rebuild it elsewhere. It is built from
sub-elements, whose nature definition do not
depend on being part of the House. However, one
cannot understand their disposition without
knowing the purpose(s) of the House.

• Soft Emergence Without disputing
• the existence of the fundamental lego building
  blocks (which may be reducible into ever-smaller
• building blocks), one argues that a complete
  description of the House (including its internal
  dynamics)
• requires more than a complete understanding of
  the lego blocks and their interactions. In
  physics this
• has led to extraordinary fruitful concepts (the
  order parameter and
• its dynamics, pattern structure formation,
  dissipative structures...
• It is often argued that similar ideas can apply
  in other areas (eg.,
• decoherence ? classical world, or even ? space
  time).

(2) Hard Emergence A much stronger view- that
the building blocks cannot be understood or even
properly defined without reference to the larger
whole (the House). For the House this is
nonsensical. It is not obviously wrong in
Quantum Mechanics. One should distinguish between
the description of a system S (in terms of a set
of constituent coordinates Qj) and the quantum
state of S, which may entangle the constituents
(so they do not have individual quantum states).
So- how do we look at this question in a formal
way in physics?
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Description using EFFECTIVE HAMILTONIANS
Heff
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Orthodox view of Heff
Ec
Scale out High-E modes
Renormalisation
Wo
Heff (Ec ) ? Heff (Wo)
The RG mantra is RG flow
fixed points
low-energy Heff
universality classes
yigt Hij(Ec) ltyj ? fagt Hab(Wo)
ltfb
Flow of Hamiltonian Hilbert space with UV cutoff
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MORE ORTHODOXY
Continuing in the orthodox vein, one supposes
that for a given system, there will be a sequence
of Hilbert spaces, over which the effective
Hamiltonian and all the other relevant physical
operators (NB these are effective operators) are
defined.
Then, we
suppose, as one goes to low energies we approach
the real vacuum the approach to the fixed
point tells us about the excitations about this
vacuum. This is of course a little simplistic-
not only do the effective vacuum and the
excitations change with the energy scale (often
discontinuously, at phase transitions), but the
effective Hamiltonian is in any case almost never
one which completely describes the full
N-particle states.
Nevertheless, most believe that the basic
structure is correct - that the effective
Hamiltonian ( note that ALL Hamiltonians or
Actions are effective) captures all the basic
physics
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RG FLOW, CRITICAL PHENOMENA, Condensed Matter
T.O.E.s
One of the main obstacles to passing from
a high-energy description of a system to a
low-energy one is the existence of phase
transitions. Physicists have turned this into a
virtue, by analysing the way the effective
Hamiltonian changes as one approaches a finite-T
critical point. One gets Universality Classes
of effective Hamiltonian, describing many
different systems, as they approach the critical
point- this means that they all have the same
form of effective Hamiltonian, differing only in
the coefficients of the operators in the
Hamiltonian.
One can also talk about T0 phase transitions- as
one changes some parameter like pressure, a
phase transtion can be induced. However here
there are no thermal fluctuations, instead we
have quantum critical fluctuations. It as been
argued with increasing vigour in recent years
that this framework may allow us to classify all
possible low-E states, thereby producing a kind
of low-energy Theory of Everything (Laughlin,
Preskill). The interesting recent theoretical
connections found between correlations in
certain 1-d models and the entanglement features
is connected with this.
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1ST CONUNDRUM- the GLASS
The simple picture of excitations perched above a
vacuum gets a rude shock when we consider Glasses
- systems with disorder frustrating
interactions. We are surrounded by these! States
pile up at low energy, but these cant
communicate with each other.
Frustrating interactions
Frustration means that at low energy, any
local change must re-organize simultaneously a
vast number of states. This forces the Hilbert
space of the effective Hamiltonian to have an
ultrametric geometry.
What this means is that no matter what energy or
temperature one is working at, the ground state
of the spin glass effective Hamiltonian is
meaningless. At finite T, the system can never
reach the ground
state, and the finite-T Hilbert space is
disconnected from any ground state. At zero-T,
the system splits into subspaces that can never
communicate with each other. Thus the effective
vacuum its structure are physically
meaningless. A glass can only be defined by its
dynamic (non-equilibrium) properties.
Ultrametric geometry of a glass Hilbert space
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2ND CONUNDRUM- the HUBBARD MODEL
The standard model of condensed matter physics
for a lattice system is the Hubbard model,
having effective Hamiltonian at electronic energy
scales given by
This apparently simple Hamiltonian has some very
bizarre properties. Suppose we try to find a low
energy effective Hamiltonian, valid near the
Fermi energy- eg., when the system is near
half-filling. We therefore assume a UV Cutoff
much smaller than the splitting U between the
Mott-Hubbard sub-bands (we assume that U gt t).
The problem is that this appears to be
impossible. Any attempt to write an effective
Hamiltonian around the Fermi energy must deal
with spectral weight transfer from the other
Hubbard sub-band- which is very far in energy
from the Fermi energy. Thus we cannot disentangle
high- and low-energy states. This is sometimes
called UV/IR mixing.
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3RD CONUNDRUM- TOPOLOGICAL FIELD THEORIES
RIGHT A statistical flux attaches itself to an
electron to make an anyon- here on a lattice
Most of the models discussed in string theory
quantum field theory are topological in nature,
with topological excitations complex vacua.
Similar models exist in condensed matter physics
(eg., FQHE).
In string theory it is hard to get rid of
tachyons, which create the analogue of a lattice
potential for the strings, leading to the
complexity of the dissipative WAH model.
A key feature of such theories, and of any
non-commutative gauge theory, is the same UV/IR
mixing we saw in the Hubbard model- ie., no
clearly-defined effective low-E action or
Hamiltonian. It is not known how general this
UV/IR mixing is.
See, eg., M. van Raamsdonk, N Seiberg hep-th/9912
072, /0002186
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Question EMERGENCE from DECOHERENCE ?
When some quantum system with coordinate Q
interacts with any other system (with coordinate
x) , the result is typically that they form a
combined state in which there is some
entanglement between the two systems.
E
Example In a 2-slit expt., the particle
coordinate Q couples to photon coordinates, so
that we have the following possibility Yo(Q)
Pq fqin ? a1 Y1(Q) Pq fq(1) a2
Y1(Q) Pq fq(2)
But now suppose we do not have any knowledge of,
or control over, the photon states- we must then
average over these states, in a way consistent
with the experimental constraints. In the extreme
case this means that we lose all information
about the PHASES of the coefficients a1 a2
(and in particular the relative phase between
them). This process is called DECOHERENCE NB 1
In this interaction between the system and its
Environment E (which is in effect performing a
measurement on the particle state), there is no
requirement for energy to be exchanged between
the system and the environment- only a
communication of phase information. NB 2 Nor is
it the case that the destruction of the phase
interference between the 2 paths must be
associated with a noise coming from the
environment- what matters is that the state of
the environment be CHANGED according to the what
is the state of the system. Question How do we
describe this for a COMPLEX SYSTEM ?
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DESCRIBING the QUANTUM-CLASSICAL BORDERLANDS
Classical Dynamics
Quantum Dynamics
Heff
Suppose we want to describe the dynamics of
some quantum system in the presence of
decoherence. As pointed out by Feynman and
Vernon, if the coupling to all the enevironmental
modes is weak, we can map the environment to an
oscillator bath, giving an effective Hamiltonian
like
A much more radical argument was given by
Caldeira and Leggett- that for the purposes of
TESTING the predictions of QM, one can pass
between the classical and quantum dynamics of a
quantum system in contact with the environment
via Heff. Then, it is arguend, one can connect
the classical dissipative dynamics directly to
the low-energy quantum dynamics, even in the
regime where the quantum system is showing
phenomena like tunneling, interference,
coherence, or entanglement and even where it is
MACROSCOPIC. This is a remarkable claim
because it is very well known that the QM
wave- function is far richer than the classical
state- and contains far more information.
Feynman Vernon, Ann. Phys. 24, 118
(1963) Caldeira Leggett, Ann. Phys. 149, 374
(1983) AJ Leggett et al, Rev Mod Phys 59, 1 (1987
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WHAT ARE THE LOW- ENERGY EXCITATIONS IN A SOLID
?
DELOCALISED Phonons, photons, magnons, electrons,

LOCALISED Defects, Dislocations, Paramagnetic
impurities, Nuclear Spins, .
.
.
..
.
.,.,
..
.
.

.

.
At right- artists view of energy
distribution at low T in a solid- at low T
most energy is in localised states. INSET
heat relaxation in bulk Cu at low T
/

.
.
,
.
..
.,
.,
.
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DECOHERENCE DYNAMICS from an EFFECTIVE H
Consider the following Heff
P.C.E. Stamp, PRL 61, 2905
(1988) NV Prokofev, PCE Stamp, J Phys
CM5, L663 (1993) NV Prokofev, PCE Stamp, Rep
Prog Phys 63, 669 (2000)
H (Wo) Dt exp(-i Sk ak.sk) H.c.
eotz (qubit)
tz wk.sk hk.sk
(bath spins)
inter-spin
interactions
At first glance a solution of this seems very
forbidding. However it turns out one can solve
for the reduced density matrix of the central
spin in all interesting parameter regimes- the
decoherence mechanisms are easy to identify
(i) Noise decoherence Random phases added to
different Feynman paths by the noise field.

(ii) Precessional decoherence
the phase
accumulated by bath spins between qubit
flips.
(iii) Topological Decoherence The phase

induced in the bath spin dynamics by the
qubit flip
itself
USUALLY PRECESSIONAL

DECOHERENCE DOMINATES
Thus decoherence can be dominated by processes
causing little or no dissipation
Precessional decoherence
Noise decoherence source
Actually the above model describes some very
interesting systems
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SOME RECENT EXPTS
Expts on Tunneling magnetic molecules Ho ions
Wernsdorfer et al, PRL 82, 3903 (1999)
and PRL 84, 2965 (2000) and Science 284, 133
(1999)
R. Giraud et al., PRL 87, 057203 (2001)
A. Morello et al. PRL 93, 197202 (2004)
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Expts on The quantum phase transition in LiHoF4
BELOW Expts on coherently Tunneling SQUIDs
H.M. Ronnow et al., Science 308, 389 (2005)
RW Simmonds et al., PRL 93, 077003 (2004)
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WARNING 3rd PARTY DECOHERENCE
This is fairly simple- it is decoherence in the
dynamics of a system A (coordinate Q) caused by
indirect entanglement with an environment E- the
entanglement is achieved via a 3rd party B
(coordinate X).
Ex Buckyball decoherence

Consider
the 2-slit expt with

buckyballs. The COM coordinate Q
of the buckyball does not couple directly to the
vibrational modes qk of the buckyball- by
definition. However BOTH couple to the slits in
the system, in a distinguishable way.
Note the state of the 2 slits, described by a
coordinate X, is irrelevant- it does not need to
change at all. We can think of it as a
scattering potential, caused by a system with
infinite mass (although recall Bohrs response to
Einstein, which includes the recoil of the 2
slit system). It is a PASSIVE 3rd party.
ACTIVE 3rd PARTY Here the system state
correlates with the 3rd party, which then goes on
to change the environment to correlate with Q.
We can also think of the 3rd party X as PREPARING
the states of both system and environment.
Alternatively we can think of the system and the
environment as independently measuring the state
of X. In either case we see that system and
environment end up being correlated/entangled.
Note the final state of X is not necessarily
relevant- it can be changed in an arbitrary way
after the 2nd interaction of X. Thus X need
not be part of the environment. Note we could
also have more than one intermediary- ie., X, Y,
etc.- with correlations/entanglement are
transmitted along a chain ( they can wiped out
before the process is finished).
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REMARKS
R1 One could argue that despite all this,
the idea that we can still think of matter as
made of elementary constituents (the lego
philosophy) is nevertheless intact. If so,
one would like to know how to formulate this in
physical theory- at the present time the
fundamental formulation of the properties of any
physical system is in terms of an effective
Hamiltonian or effective action- and this poses
the problems discussed herein.
R2 These are not just condensed matter
physics problems- they also arise in high energy
physics Notice that whereas the IR / UV
mixing comes in in condensed matter systems
typically in the presence of a lattice, this is
not necessary- eg., in non-commutative gauge
theory or open string theory there is no lattice.
In any case- since all Hamiltonians are
effective, the problems we address seem to be
generic to all many-body quantum theories, in
condensed matter, particle theory, or quantum
gravity.
R3 Some of the problems discussed so far
exist in a classical theory. However features
like IR / UV mixing seem to be quantum
mechanical. And of course, the ineluctable role
of entanglement is entirely a QM feature.
Note that some formulations of QM make the
description of any quantum system dependent on
macroscopic objects, and their entanglement with
them (eg., Copenhagen/Bohr).
R4 Quantum Mechanics is a much richer
theory than classical mechanics- and Q states
contain much more information. This feature
appears in the Quantum/Classical borderlands when
one looks at mechanisms and sources of
decoherence- many of the most potent sources of
decoherence do not have a classical dissipative
analogue, are not connected with the noise
spectrum, hardly affect the classical
dynamics.
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TALK see http//physics.ubc.ca/stamp