different symmetry realizations in relativistic coupled bose systems at finite temperature and...
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Different symmetry realizations in relativistic coupled Bose systems
at finite temperature and densities
Collaborators: R.L.S. Farias and R.O. Ramos
Rodrigo Vartuli
Department of Theoretical Physics,Department of Theoretical Physics, UERJII Latin American Workshop on
High Energy Phenomenology
5th December 2007São Miguel das Missões, RS,
Brazil
Outline• Motivation
• Study of symmetry breaking (SB) and symmetry restoration (SR)
• In multi-scalar field theories at finite T and are looking for the phenomena
* symmetry nonrestoration (SR) * inverse symmetry breaking (ISB)
• How a nonzero charge affects the phase structure of a multi-scalar field theory?
• Work in progress and future applications
1- Motivation1- MotivationThe larger is the temperature, the larger is the The larger is the temperature, the larger is the
symmetrysymmetrythe smaller is the temperature, the lesser is the the smaller is the temperature, the lesser is the
symmetry:symmetry:
Symmetry Breaking/Restoration in O(N) Scalar Models
Boundness:
+ unbroken
- broken0
Relativistic case:
The potential V( ) for –m2, N=1 (Z2)
Let´s heat it up!!
Thermal Mass at high-T and N
M ²(N=2)
For ALL single field models:
Higher order corrections do NOT alter this pattern !!
(1974)
O(N)xO(N) Relativistic Models
Boundness: λ>0 OR: λ<0!!
Thermal masses to one loop
Critical Temperatures at high-T and N=2
or i
M² (N=2)
Both m² < 0:SR in the ψ sector
SNR in the sector
Transition patterns
M ²
ISB
Transition patterns
Both m² > 0: sector:
unbroken sector : ISB
Temperature effects in multiscalar field models Temperature effects in multiscalar field models can change the symmetry aspects in unexpected ways:can change the symmetry aspects in unexpected ways:
e.g. in the O(N)xO(N) example, it shows the possibilities e.g. in the O(N)xO(N) example, it shows the possibilities of phenomena like inverse symmetry breaking (ISB)of phenomena like inverse symmetry breaking (ISB)
and symmetry nonrestoration (SNR)and symmetry nonrestoration (SNR)
But be careful:
Question: Can we trust perturbative methods Question: Can we trust perturbative methods at high temperatures ?at high temperatures ?
NO ! (but these phenomena appear too in nonperturbative
approaches) THEY ARE NOT DUE BROKEN OF PERTURBATION THEORY
~ O( T ) ~ O( T . T/m )
Perturbation theory breaks down for Perturbation theory breaks down for temperatures temperatures l T/m > 1
2 2
Requires nonperturbation methods: Requires nonperturbation methods: daisy and superdaisy resum, daisy and superdaisy resum,
Cornwall-Jackiw-Tomboulis method, Cornwall-Jackiw-Tomboulis method, RG, RG,
large-N, large-N, epsilon-expansion,epsilon-expansion,
gap-equations solutions, lattice, etcgap-equations solutions, lattice, etc
Nonperturbative methods are quite discordant aboutthe occurrence or not of ISB/SNR phenomena:
NONO
PLB 151, 260 (1985), PLB 157, 287 (1985), PLB 151, 260 (1985), PLB 157, 287 (1985), Z. Phys. C48, 505 (1990)Z. Phys. C48, 505 (1990)
Large-N expansion Large-N expansion
Gaussian eff potential Gaussian eff potential PRD37, 413 (1988), Z. Phys. C43, 581 (1989) PRD37, 413 (1988), Z. Phys. C43, 581 (1989)
Chiral lagrangian method Chiral lagrangian method
Monte Carlo simulations Monte Carlo simulations
PRD59PRD59,025008 (1999),025008 (1999)
Bimonte et al NPB515, 345 (1998),Bimonte et al NPB515, 345 (1998), PRL81, 750 (1998)PRL81, 750 (1998)
Large-N expansion Large-N expansion
Gap equations solutions Gap equations solutions PLB366, 248 (1996), PLB388, 776 (1996), PLB366, 248 (1996), PLB388, 776 (1996),
NPB476, 255 (1996) NPB476, 255 (1996)
Renormalization Group Renormalization Group
Monte Carlo simulations Monte Carlo simulations
PRD54, 2944 (1999), PLB367, 119 (1997)PRD54, 2944 (1999), PLB367, 119 (1997)
Bimonte et al NPB559, 103 (1999),Bimonte et al NPB559, 103 (1999),Jansen and Laine PLB435, 166 (1998)Jansen and Laine PLB435, 166 (1998)
YESYES
PLB403, 309 (1997) PLB403, 309 (1997)
Optimized PT (delta-exp) Optimized PT (delta-exp) M.B. Pinto and ROR, PRD61, 125016 (2000)M.B. Pinto and ROR, PRD61, 125016 (2000)
Conclusions for O(N)xO(N) relativistic:ISB/SNR are here to stay!! Applications?
Cosmology, eg, Monopoles/Domain Walls
What happens in real condensed matter systems ?
((potassiumpotassium sodium tartrate tetrahydrate) sodium tartrate tetrahydrate)Liquid crystalsLiquid crystals
(SmC*)(SmC*)Reentrant phaseReentrant phase383K < T < 393K383K < T < 393K
Manganites: (Pr,Ca,Sr)MnO ,Manganites: (Pr,Ca,Sr)MnO ,ferromagnetic reentrant phase above the Curie ferromagnetic reentrant phase above the Curie
temperature (colossal magnetoresistence)temperature (colossal magnetoresistence)
Inverse melting (~ ISB) liquid Inverse melting (~ ISB) liquid crystal: crystal: He3,He4, He3,He4,
binary metallic alloys (Ti, Nb, Zr, Ta) binary metallic alloys (Ti, Nb, Zr, Ta) bcc to amorphous at high T bcc to amorphous at high T
Etc, etc, etc ….Etc, etc, etc ….
33
Review: cond-mat/0502033Review: cond-mat/0502033
Phase structure and the effective potential at fixed
chargeWe start with the grand partition function
Where H is the ordinary Hamiltonian and
Using the standard manipulations like Legendre transformations … we get
Phase structure and the effective potential at fixed
chargeZ is evaluated in a systematic way
where
or
where
Phase structure and the effective potential at fixed
chargeUsing imaginary time formalism
The renormalized effective potential in the high density and temperatures is given by
where
Neglecting the zero point contribution similar made in PRD 44, 2480 (1991)
or
Phase structure and the effective potential at fixed
chargeThe phase structure depends on the minima of the effective potential
We have two minima:
for unbroken symmetry
for broken symmetry
and
Phase structure and the effective potential at fixed
chargeMinimizing the effective potential with respect to µ
In the high density limit µ >> m
Now we will show numerical results for broken
and unbroken phase of the theory with one complex scalar field
Working at high density µ >> m and high temperature T
0mfor !42
1 2422 mU
Numerical Results (broken phase)
PRD 44, 2480 (1991)Small charge - Symmetry restored
Charge increase - Symmetry never restored (SNR)
Numerical Results (unbroken case)
Unbroken case 02 m Ordinary η=0 have no Symmetry breaking
But at high T and µ
Remember that
0mfor !42
1 2422 mU
Numerical Results (unbroken case)
PRD 44, 2480 (1991)Broken symmetry at high T
(ISB)
In Preparation
& For one complex scalar field we showvery interesting results like(PRD 44, 2480 (1991))
Symmetry non restorationInverse symmetry breaking
& We are extending these calculations for two complex scalar fields
Future applications
* In collaboration with L.A. da Silva R.L.S. Farias and R.O. Ramos
Nonequilibrium dynamics of multi-scalar field Theories
• Markovian and
• Non-Markovian evolutions for the fields…
See poster: Langevin Simulations with Colored
Noise and Non-Markovian Dissipation
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