id sid tid token lemma pos h989r210119 1 1 sampling sample VERB h989r210119 1 2 the the DET h989r210119 1 3 configuration configuration NOUN h989r210119 1 4 space space NOUN h989r210119 1 5 of of ADP h989r210119 1 6 complex complex ADJ h989r210119 1 7 biological biological ADJ h989r210119 1 8 molecules molecule NOUN h989r210119 1 9 is be AUX h989r210119 1 10 an an DET h989r210119 1 11 important important ADJ h989r210119 1 12 and and CCONJ h989r210119 1 13 formidable formidable ADJ h989r210119 1 14 problem problem NOUN h989r210119 1 15 . . PUNCT h989r210119 2 1 one one NUM h989r210119 2 2 major major ADJ h989r210119 2 3 difficulty difficulty NOUN h989r210119 2 4 is be AUX h989r210119 2 5 the the DET h989r210119 2 6 high high ADJ h989r210119 2 7 dimensionality dimensionality NOUN h989r210119 2 8 of of ADP h989r210119 2 9 this this DET h989r210119 2 10 space space NOUN h989r210119 2 11 , , PUNCT h989r210119 2 12 roughly roughly ADV h989r210119 2 13 $ $ SYM h989r210119 2 14 3n$ 3n$ NUM h989r210119 2 15 , , PUNCT h989r210119 2 16 with with ADP h989r210119 2 17 the the DET h989r210119 2 18 number number NOUN h989r210119 2 19 of of ADP h989r210119 2 20 atoms atom NOUN h989r210119 2 21 $ $ SYM h989r210119 2 22 n$ n$ X h989r210119 2 23 typically typically ADV h989r210119 2 24 in in ADP h989r210119 2 25 the the DET h989r210119 2 26 thousands thousand NOUN h989r210119 2 27 . . PUNCT h989r210119 3 1 this this DET h989r210119 3 2 thesis thesis NOUN h989r210119 3 3 introduces introduce VERB h989r210119 3 4 shadow shadow NOUN h989r210119 3 5 hybrid hybrid PROPN h989r210119 3 6 monte monte PROPN h989r210119 3 7 carlo carlo PROPN h989r210119 3 8 ( ( PUNCT h989r210119 3 9 shmc shmc PROPN h989r210119 3 10 ) ) PUNCT h989r210119 3 11 , , PUNCT h989r210119 3 12 a a DET h989r210119 3 13 propagator propagator NOUN h989r210119 3 14 through through ADP h989r210119 3 15 phase phase NOUN h989r210119 3 16 space space NOUN h989r210119 3 17 that that PRON h989r210119 3 18 enhances enhance VERB h989r210119 3 19 the the DET h989r210119 3 20 scaling scaling NOUN h989r210119 3 21 of of ADP h989r210119 3 22 sampling sample VERB h989r210119 3 23 with with ADP h989r210119 3 24 space space NOUN h989r210119 3 25 dimensionality dimensionality NOUN h989r210119 3 26 . . PUNCT h989r210119 4 1 shmc shmc PROPN h989r210119 4 2 is be AUX h989r210119 4 3 a a DET h989r210119 4 4 biased biased ADJ h989r210119 4 5 variation variation NOUN h989r210119 4 6 on on ADP h989r210119 4 7 the the DET h989r210119 4 8 hybrid hybrid PROPN h989r210119 4 9 monte monte PROPN h989r210119 4 10 carlo carlo PROPN h989r210119 4 11 algorithm algorithm PROPN h989r210119 4 12 ( ( PUNCT h989r210119 4 13 hmc hmc PROPN h989r210119 4 14 ) ) PUNCT h989r210119 4 15 that that PRON h989r210119 4 16 uses use VERB h989r210119 4 17 an an DET h989r210119 4 18 approximation approximation NOUN h989r210119 4 19 to to ADP h989r210119 4 20 the the DET h989r210119 4 21 modified modify VERB h989r210119 4 22 hamiltonian hamiltonian NOUN h989r210119 4 23 to to PART h989r210119 4 24 sample sample VERB h989r210119 4 25 more more ADV h989r210119 4 26 efficiently efficiently ADV h989r210119 4 27 through through ADP h989r210119 4 28 phase phase NOUN h989r210119 4 29 space space NOUN h989r210119 4 30 . . PUNCT h989r210119 5 1 the the DET h989r210119 5 2 overhead overhead NOUN h989r210119 5 3 introduced introduce VERB h989r210119 5 4 is be AUX h989r210119 5 5 modest modest ADJ h989r210119 5 6 in in ADP h989r210119 5 7 terms term NOUN h989r210119 5 8 of of ADP h989r210119 5 9 time time NOUN h989r210119 5 10 , , PUNCT h989r210119 5 11 involving involve VERB h989r210119 5 12 only only ADV h989r210119 5 13 dot dot NOUN h989r210119 5 14 products product NOUN h989r210119 5 15 of of ADP h989r210119 5 16 the the DET h989r210119 5 17 history history NOUN h989r210119 5 18 of of ADP h989r210119 5 19 positions position NOUN h989r210119 5 20 and and CCONJ h989r210119 5 21 momenta momenta NOUN h989r210119 5 22 generated generate VERB h989r210119 5 23 by by ADP h989r210119 5 24 the the DET h989r210119 5 25 integrator integrator NOUN h989r210119 5 26 . . PUNCT h989r210119 6 1 we we PRON h989r210119 6 2 present present VERB h989r210119 6 3 the the DET h989r210119 6 4 derivation derivation NOUN h989r210119 6 5 of of ADP h989r210119 6 6 shmc shmc PROPN h989r210119 6 7 , , PUNCT h989r210119 6 8 along along ADP h989r210119 6 9 with with ADP h989r210119 6 10 : : PUNCT h989r210119 6 11 proof proof NOUN h989r210119 6 12 that that SCONJ h989r210119 6 13 it it PRON h989r210119 6 14 preserves preserve VERB h989r210119 6 15 microscopic microscopic ADJ h989r210119 6 16 reversibility reversibility NOUN h989r210119 6 17 ; ; PUNCT h989r210119 6 18 analysis analysis NOUN h989r210119 6 19 of of ADP h989r210119 6 20 the the DET h989r210119 6 21 asymptotic asymptotic ADJ h989r210119 6 22 speedup speedup NOUN h989r210119 6 23 of of ADP h989r210119 6 24 shmc shmc PROPN h989r210119 6 25 over over ADP h989r210119 6 26 hmc hmc PROPN h989r210119 6 27 , , PUNCT h989r210119 6 28 which which PRON h989r210119 6 29 is be AUX h989r210119 6 30 shown show VERB h989r210119 6 31 to to PART h989r210119 6 32 be be AUX h989r210119 6 33 $ $ SYM h989r210119 6 34 o(n^{1/4})$ o(n^{1/4})$ NOUN h989r210119 6 35 when when SCONJ h989r210119 6 36 using use VERB h989r210119 6 37 verlet verlet ADJ h989r210119 6 38 integrators integrator NOUN h989r210119 6 39 ; ; PUNCT h989r210119 6 40 and and CCONJ h989r210119 6 41 results result NOUN h989r210119 6 42 evaluating evaluate VERB h989r210119 6 43 correctness correctness NOUN h989r210119 6 44 and and CCONJ h989r210119 6 45 efficiency efficiency NOUN h989r210119 6 46 . . PUNCT