Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged...

14
MD Simulation of Coulomb Crystals Thierry Matthey, para//ab, UNIFOB, University of Bergen c Thierry Matthey, Fevik Metting, August 30, 2002. MD Simulation of Coulomb Crystals 1/ ??

Transcript of Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged...

Page 1: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

MD

Sim

ulationofC

oulomb

Crystals

Thierry

Matthey,para//ab,U

NIF

OB

,University

ofBergen

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

1/??

Page 2: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

What

areC

oulomb

crystals?�

Asystem

ofpositivecharged

ions(1-����

)trapped

bya

magnetic

field.

++

+

Acandidate

forQ

uantumP

rocessors.

Apossibility

tostudy

stronglycoupled

systems

with

onlypositive

charges.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

2/??

Page 3: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Experim

ents

Left:M

onocomponent,sphere.

Right:

Bicom

ponent,string,Ca ���

(Blue),M

g ��

(Red).

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

3/??

Page 4: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Physicalm

odel���

Quantum

Mechanics

and ����

signifi-cant.

��� K

ClassicalA

pproximation�

Classical

Molecular

Dynam

ics(N

ewton’s

equationofm

otion)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

4/??

Page 5: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Physicalm

odel(cont.)

Q2

Q1

Rm

,q

Coul �

����� � �����

� �

Trap ��

!

.

Coul ��

Trap�

!�#"$% ������'& ��� ()* �+.

NB

:Independentof ��

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

5/??

Page 6: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Research

�Investigation

ofthestructure

anddynam

icsofso-

calledions

trappedin

aelectric

andm

agneticfield

(PaulTrap)

with

1- ��,�

ions.

Radial

distributionand

shellstructure

(ornot)

ofm

ono-and

bicomponent(C

a ���

andA �-�

)crystals.

Dynam

icalfeaturesoffinite

temperature

(�� K).

Future

work:

Fulltreatm

entofquantaleffects.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

6/??

Page 7: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Molecular

Dynam

ics(M

D)

�. /

/ 0 12.3 04 � 1�.3 04657 // 0

12.3 04

(1)

// 07 �83 5

equlibrium4

(2)

1�. � 59.;:

(3)

:��<=>�?@

.BA�CDFE. G

. GDHHHHH HHHHH 12.D HHHHH HHHHH I

�J ?@. A� �. 12 .

(4)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

7/??

Page 8: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Molecular

Dynam

ics(M

D)

(cont.)

New

ton’sequation

ofmotion

solvedby

thenum

ericalLeap-Frog

method

with

Nose-H

oovertherm

ostat:

KML� ���KMLON �� 5

P0� "$$% � L5

7 LKML N �� ())*

(5)/7 L� ��

/ 0

�Q "

$$$% ?@. A� �.3 K L� ��.4 5

R SJTU ()))*

(6)

2 L� ��2 LIP0KVL� ��

(7)

7 L� ��7 LIP0 /7 L� ��

/ 0W

(8)

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

8/??

Page 9: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

PR

OT

OM

OL

–a

moleculardynam

icsfram

ework

�A

nobject-oriented

component

basedfram

ework

form

oleculardynam

icssim

ulations.

Designed

forhigh

flexibility,easyextendibility

andm

aintenance,andhigh

performance

demands,in-

cludingparallelization.

Supportofm

ultipletim

e-steppingintegration.

Fastelectrostatic

forceevaluation

algorithms

likeplain

Ew

ald(X3 S

+�4 ),P

article-Mesh-E

wald

(X3 SYZ[ S4 ),and

Multigrid

summ

ation(X3 S

4 ).

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

9/??

Page 10: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

PR

OT

OM

OL

–a

moleculardynam

icsfram

ework

(cont.)

libparallel, libforceslibbase, libtopology

libintegrators

libfrontendC

omponent

Fram

ework

Class Library

Middle Layer

Front−

end

Back−

end

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

10/??

Page 11: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Fronthem

isphereofthe

outershell

Left:S

ystemofa

20,288C

a

\]^ .R

ight:S

ystemofa

10,144C

a

\]^ _a`b

and10,144

A c\d^ _aebsystem

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

11/??

Page 12: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Radialdistrib

utionofm

ono-andbicom

ponentcrystals

050

100150

200250

0 1 2 3 4 5 6

Radius (µm

)

Density

0100

200300

4000

0.5 1

1.5 2

2.5 3

Radius (µm

)

Density

Left:20,288

Ca

\]^

(Blue),

and10,144

Ca

\]^

and10,144

A c\d^

(Green),

and

20,288A c\d^

(Red)

ions.R

ight:100,000

Ca

\]^(B

lue),and

50,000C

a

\]^

and

50,000A c\d^

(Green)

ions.T

heinner

parthasbeen

smoothed.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

12/??

Page 13: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Conclusions

Sim

ulationsresult

inclear

outershellstructure

inlarge

bicomponent

ioncrystals

with

identicalGf �

ration.

Each

component

haveslightly

differentshellradii

resultingin

aninteresting

“doublestructure”ofeach

shell.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

13/??

Page 14: Simulation of - ii.uib.nomatthey/ttp5/ttp_protomol_presentation4.pdf · system of positiv e charged ions (1-) tr apped b y a magnetic field. + + + A candidate f or Quantum Processors.

Partners

JanP

etterH

ansen,University

ofBergen.

MichaelD

rewsen,T

heion

Trapgroup,Institute

ofP

hysicsand

Astronom

y,University

ofAarhus.

PR

OT

OM

OL

isa

collaborationw

orkw

ithJesus

A.

Izaguirre,CS

E,U

niversityofN

otreD

ame,U

SA

.

c�

Thierry

Matthey,F

evikM

etting,August30,2002.

MD

Sim

ulationofC

oulomb

Crystals

14/??