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by: Heath Hane III


Heath Hane III
GPA 3.82


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Class Notes
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This 20 page Class Notes was uploaded by Heath Hane III on Saturday September 12, 2015. The Class Notes belongs to PHYS 8900 at University of Georgia taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/202492/phys-8900-university-of-georgia in Physics 2 at University of Georgia.




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Date Created: 09/12/15
First Signs of the Transition Between Quantum and Classical Dynamics Phys Rev Lett 99 040404 2007 PHYS 8900 Journal Club 9 2007 Daniel Seaton Motivation NEMS bring us closer to testing l 7 basic principles of quantum mech Experiments want to nd rst signs of quantum domain as mass and temperature are decreased Mass decreasing natural freq increasing l GHZ Thermal and quantum energy comparison g Mom 325 uyyszuyxvzoszs 7 Numerical calculations can lead the way for experiment Ron Lifshitz Tel Aviv Univ When looking for quantum effects in vibrating objects IImost researchers are trying to go directly for holy grailsquot says LifshitzThey39re looking for exotic effects that might not be observable for years he says Instead his team simply calculated the rst signatures of a transition from classical to quantum behavior as the mass and temperature of a vibrating object decrease Watching an Object go Quantumquot Phys Rev Focus 20 2 2007 Introduction to NEMS Duf ng nonlinear oscillator 0 Numerical calculations 39 Classical and Quantum Results Conclusions NEMS O Nanoelectromechanical systems M L Roukes Caltech Technical Digest of the 2000 Solid State Sensor and Actuator Workshop httpenwikipediaorgwiki Image U Nanomotorgif 2 httpctcpmasseyacnzzuelicke Logo CTCRipg mgelergrouphtm Duf ng Nonlinear Oscillator 0 Damped and Driven X 5x I 92x 8x3 FCOSDt 0 Bistability 0 Activation Tunneling 0 Statistical Mechanics 2 htt enwiki ediaor wikiBistable F C Moon Phys Rev Lett 53 962 I984 Parameters and Dimensions 0 Scaled Units mass and natural freq I 0 Effective 72 39 Classical when effective h gt O 0 Unpublished reference 3 39 httparxivorgabsquantphO702l74 ml DO 72 x0 mwo a u m r U 1 TI 4 4 NJ 1 w a 7 4 3 x 4 0 Classical Calculation 39 Initial state I04 points drawn from Gaussian 39 httpwwwmathudeleduhsiaom302 JavaToolsosduffnghtml 39 Classical phase space distribution 0 Quantum Calculation 39 Initial state coherent state 39 Integrate schrodinger equation using truncated harmonicoscillator energy basis 39 Wigner function Numerical Calculations 0 Quantum Wigner Function 1 mm dx e QlW ltxx lptlx x gt 0 Wigner function is not a true probability distribution 0 Negative values occur where there is no classical analog 0 However we can still get a standard probability Pxt Wxptdp Physical Situations 0 Three regimes Isolated Resonator 2 Tenv 0 coupled to heat bath 3 Tenv gt 0 coupled to heat bath k T 0 Heat bath using Langevin approach En1122 ET 39 adds two terms to each calculation 39 I dissipative velocity 2 random force 4 5mm 0 Simple Example NoseHoover thermostat x W T Hee e ed Reematew a PM U effective 72 02 l 3339 I J 11 initial Czuhcrcut state i0 2111 300139 Isolaijt ed Resonator Animations TW 3 Hm F ng i2 Tenv 0 effective h 01 a Initial coherent 51311 I J 39Ter39w39 0 Heat Bath Fig2quot e Tenv 2729 effective h 01 39a39j Inilial coherent 5mm ramp 39T nvv39gt 0 Heat Bath 4 0 Fig a same as in Fig 3 only for classical calculation kBTenv 0 Authors hope that these results can offer a first step for experiments Connection to Experiment 0 Current NEMS resonators m 210 18 kg 2108 Hz and ac 210 9 m This implies 0 Suspended Nanotubues PossibleVaIues m 210 2115 2108 Hz and ac 210 11m This implies heff2 10 S U p a di NM gtWE C Nature London 43 I 284 2004 Nano Lett 6 2904 2006 lt5quot 4L Em C These are initial results 0 Authors plan to continue this type of work 39 Want to study the switching between states httpctcpmassexacnzlzuelicke 39 Tunneling Activation Logo CTCR39pg 0 Experiments are close authors expect veri cation in near future Q 8 9 0 I I O cg 2


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